Magic items of the same rarety are supposed to be roughly (not exactly) even in terms of how much they affect the game. But some could favor damage, some defence, some spellcasting options, or any combination, so they cant always be directly compared.
The acheron blade for example is basically a +1 weapon with 2 once per day abilities (1 for defense, 1 for debuffing). Compared to a +2 weapon, it will do less damage, but is more versatile.
Globally it's the same, but more in the details they might benefit one character more in some situations. Just be aware that these are very rough classifications and that there are some items in the rules that really are not in the right category if you consider it purely in terms of power. I can only advise looking at the tables here to get an idea of the gp value, which is at least a bit more accurate:
Acheron Blade strikes me as an NPC weapon that would be logically found in the hand of a vampire because of the immunity to turn undead it gives.
It's day abilities are so-so and you are trading them for a +1 to attack and damage AND attunement slot (a +2 weapon requires no attunement, AB does).
If you want the most egregious example of difference between two items of the same rarity, just consider that a Wand of Polymorph has the same rarity as Staff of Power.
I want to know if all weapons of the same rarity have the same improvement to the player
example
If a weapon +2 is equivalent to an Acheron blade. (Both rare)
Thanks for helping me
Depends on what you mean by "improvement".
Magic items of the same rarety are supposed to be roughly (not exactly) even in terms of how much they affect the game. But some could favor damage, some defence, some spellcasting options, or any combination, so they cant always be directly compared.
The acheron blade for example is basically a +1 weapon with 2 once per day abilities (1 for defense, 1 for debuffing). Compared to a +2 weapon, it will do less damage, but is more versatile.
Link isn't working?
Absolutely not.
Acheron Blade strikes me as an NPC weapon that would be logically found in the hand of a vampire because of the immunity to turn undead it gives.
It's day abilities are so-so and you are trading them for a +1 to attack and damage AND attunement slot (a +2 weapon requires no attunement, AB does).
If you want the most egregious example of difference between two items of the same rarity, just consider that a Wand of Polymorph has the same rarity as Staff of Power.
It could also be because this is the link address you used: "https://www.dndbeyond.com/forums/dungeons-dragons-discussion/tips-tactics/And yet, you have agreed that spells like hold person can't be cast through a wall of force."
Might want to edit that and replace it with the Google doc.