is it better, worse or about the same power wise compared to similar classes? would the difference in power level be noticeable in adventure that goes from levels 1 to 7, or one going from levels 1 to 13? (assuming no multiclassing and minimal build schenanigans from all players)

I feel like the class became a lot more mature with the second major iteration. There were ten revisions of the class prior to the major one. That being said, the four subclasses are so varied from each other, it makes it difficult to judge class-wide balance.

I honestly think that the class got stronger with its most recent iteration, but before that it was a woefully weak class that only really was useful for highly specific Mutant builds designed to break systems. Now, I think it's much easier to just play a Bloodhunter without looking for a way to break it in service of something else.... because essentially the class is already a multiclass of several other classes, functioning as a hybrid of some of the flavors you'd expect to find in Paladin, Ranger, Rogue, and Warlock. 

TLDR... you're going to be an excellent striker, and possibly throw out some clutch Maledicts that make a boss battle go very well for your party, but your middling AC and HP-itensive class features and poor saves are going to hold you back from feeling stronger than the rest of the party, they'll have plenty of opportunities to come to your rescue. In my eyes, the best DPR subclass is probably Profane Soul or Ghost Slayer, the best all-arounders-without-gimmicks are Mutant or Ghost Slayer, and the most defensive are Lycan or Profane Soul. But on top of all of that combat, the class also has several lore/tracking/exploration ribbons that will make you feel like a robust member of the party and not just a weapons system. 

Base Class-

• Pros:
  • Three skills instead of the usual two, plus a Tool. 
  • The extra elemental damage from Crimson Rite starts off about tracking a Rogue's Sneak Attack, but will fall off in Tiers 3 and 4 (unless Two-Weapon Fighting, then it might keep up, and Ghostslayer can bump it up higher against certain opponents).  
  • The Brand at 6 bumps DPR up a very little bit further, as long as you're playing a melee front liner, but is really more about its ribbon abilities than the damage. 
  • Dark Augmentation at 10 is a nice Paladin-esque bump to saves, but the fact that it doesn't help the Lycan with its losing battle against Wisdom saves makes me laugh. 
  • Blood Maledicts are very effective abilities that can change the swing of battle... but with only one or two per battle, they're more effective in boss battles than they will be in other larger combats throughout the day. The Binding one is the only one that has real potential to catch your DM off guard and frustrate them. 
• Cons:
  • DCs are Intelligence based, which somewhat constrains race choices and doesn't synergize well with multiclassing.
  • Only Medium armor, for a class that wants to be in melee, is an awkward and stat-intensive limitation. Medium armor makes Strength builds more difficult, or requires accepting lower AC (see below)
  • Doesn't have the Defense fighting style as an option, which would be a very good one for melee characters stuck in medium armor, meaning you really are going to need to take a Feat and/or sacrifice DPR by using a Shield if you want to get into the "good" AC range of 18+
  • Intelligence save proficiency, which is one of the least valuable saves to have. 

Subclasses-

• Ghostslayer:
  • Doesn't significantly change how the class plays, just makes it all around "better" against Undead, with a couple of mobility ribbons. Honestly, this subclass is more about being able to run through walls than it is about killing undead, and about being able to burst down your Brand-ed enemy even faster once/short rest, killing Undead faster is just icing on top of that cake. This subclass is like the Mutant, in that it really doesn't give you a new playstyle, but it does make you a little better at doing what you're already doing as a BH (delivering high damage to high value targets). 
•  Lycan:
  • Adds Monk and Barbarian flavors into the class... but only while transformed, which is limited enough that you won't be transformed in every fight, and really leaves ranged BH's in the cold (though, they're already not what the class is about). Shores up a Str BH's poorer AC a little bit, but is just as good for Dex BH. The major drawback is that going berzerk is keyed to Wisdom saves (even if the DC is pretty low), which is not ideal since your class doesn't have those, and Wisdom is a dump stat for you in line behind Dex, Intelligence, (possibly Strength if you don't want to use finesse weapons), and Constitution. To assure that you pass these, Resilient (Wisdom) is enough to drop it from a 40/60 risk to like a 5/95 chance.. but that further feat-taxes the class. Honestly, the best approach I've found is to just either not even try to pass those saves and just plan your movement accordingly so that it isn't an issue (meaning Barbarian is a better multiclass for this subclass than it first appears, though Monk is even better!)... or start life as a Monk. :)
• Mutant: 
  • Really this subclass is just about "have a Dexterity or Strength or Intelligence modifier +1 or +2 higher than you ought to." But, the base class is already fairly feature-dense, so that isn't a bad thing, and Mutants are perhaps the most effective all-around subclass as a result, with no real meaningful drawback like the Lycan has. There may come times when you temporarily want to use a different mutagen, but most likely either Potency or Celerity or Sagacity will be your assumed default for the entirety of your career, and that's okay! 99% of what we do is make Dexterity or Strength-based attacks, so why not be better at landing them than every other PC character is allowed to be? 
• Profane Soul:
  • Warlocks are tricky to play as casters, given how few slots you have, but that's somewhat compensated by the fact that when they do cast a spell it's at max slot level. Profane Souls have the limited slots of a warlock, but a pretty slow slot level progression, so.... really you're going to probably be using those slots for utility/buff spells, not damage. Which is fine, because the base class features are already specialized for melee DPR, except that the base Warlock spell list isn't great for self-buff spells or utility casting (no Shield, no Haste, etc.), and you aren't proficient with Constitution saves to pass Concentration checks. The Undying is head and shoulders above the other pact choices here, since it shores up a major weakness of the base class (burning through AC from using features and low AC), triggered on playing into its strength (killing things with melee attacks). The others are... meh. The ability to follow a cantrip (Green-Flame Blade or Booming Blade) with a weapon attack as a Bonus Action is much better on this guy than it is on the Fighter's Eldritch Knight, since you're sacrificing fewer Attack Action attacks to do so as a BH. At the end of the day, just take this subclass to be a better melee fighter with a SCAG cantrip in your rotation, some self-healing in melee as an Undying, and Hex, Misty Step or Mirror Image, and Counterspell or Fly.

so, would playing a zariel tiefling profane soul (of the fiend) who picks up the flames of peletegros feat to create an fantastic fire aura that deals 1d4 fire damage to the attacker whenever somebody hits me in melee (as long as i keep casting green flame blade) make up for poor armor class or just worsen my problem?

Hmmm. A Zariel tiefling gives you no bonuses to Dexterity or Strength, and Flames of Phlegethos bumps your Intelligence. Are you trying to be a cantrip caster? 

At level 5, having put 15's into Dex, Con, and Intelligence, and Flames of Phlegethos at 4, you'd only have AC 17 if you want to keep a hand free for casting Somatic and Material component spells (side note: Profane Souls don't get spell focuses, so you'll want a spell component pouch), or AC 19 with a Shield. Green-flame Blade itself might be just about the only useful spell on the low-level Warlock list I can think of that you'd have selected (and Cause Fear, I suppose) that wouldn't be prevented from wearing a shield, so that sort of presumes that you're dueling with a one-handed weapon, or are using a two-handed weapon. Two-handed weapons can't be finesse, so that leaves you with a Rapier, with a crappy +2 dex modifier to hit. Hanging back to throw Fire Bolt instead would use your better +3 Intelligence modifier... but make Flames of Phlegethos and most of your Blood Hunter features irrelevent. 

Is d4 damage (average 2) going to be enough to discourage T2+ enemies from focusing down the AC 17 guy with only 30 hit points left who is in their face doing... 1d8+1d8(reroll 1's and 2's)+1d6 (reroll 1's and 2's) +2 +2 per attack (average 19, or 22 if you add a Hex on there too) with a flaming sword? Maybe, maybe not... I think you might end up a fairly popular target, though a little less so if you're skipping Hex and wielding a Shield instead. But, you're basically at a -2 to hit from where you ought to be as a melee character, because you only have a 15 in your primary attack stat, woof. 

I still think that the Undying patron would be a little more mechanically beneficial for you (giving you healing, and a spell at higher levels that doesn't interfere with holding a Shield), instead of the Fiend (which really only adds about 1 average damage to a hemocraft roll, and provides you spells at higher levels that require you to have a free hand not wielding a shield to cast). Or, leaning into being "fire guy" by being a Ghostslayer instead, since that class lets you deal more hemocraft damage to undead and targets of your Brand. Or, be a Mutant, to shore up the sub-par Dexterity that being a Tiefling with a fluffy feat has left you. 

I would say that the blood hunter is pretty well balanced. Like TexasDevin said all of the subclasses are so varied it makes it difficult to judge, but even with that each of the subclasses are balanced within their own right. Order of the Lycan's can deal really consistent damage levels 1-7, like 3d6 plus 12 (1d6+4 per attack if your prioritize dex or str) plus 3d6 Rite Damage. But they also have to worry about turning on their allies, and the rite damage can really start stacking up. Order of the profane soul adds some fun tools, the only downside is the lack of spell slots but that's a really good balancing act. Order of the Ghost Slayer is super good against undead monster types, and decent against others. The only downside is the rite damage starts stacking up, but same thing with the lycans it's a balancing act. The only one that might be "broken" would be order of the mutant just because some of the buffs in the class are broken. Such as a flat +3 to Dex or Int, but the downsides balance it out. 
Overall i'd say Matt Mercer did an excellent job balancing the class, and it manages to keep up with mid to high tiers classes just fine.