As a fighter or paladin class with multiple attacks is green flame bade effective 

Quote from rakassan101 >>

As a fighter or paladin class with multiple attacks is green flame bade effective 

For a Fighter, generally not, except perhaps for an Eldritch Knight, who can cast it and also make a weapon attack by level 7. For a Paladin it probably isn't the best. The ones who use the blade cantrips the best are either Rogues who want to stack that and Sneak Attack into one big hit or the Eldritch Knight 7/Bladesinger 6 multiclass who can make a weapon attack and then make two blade cantrip attacks.

Depends on the problem.

Assuming 5th level, and ignoring class abilities for now, you either are :

1. rolling twice with each hit being weapon damage + stat bonus,
2. or rolling once and getting weapon damage + stat bonus + 1d8 on a target, and 1d8 + stat bonus on a second target.

However how much damage you do, is dependent on the AC.  Against a high AC, you have a better chance of doing damage in case 1 than case 2 due to probability.  However, if you are using GFB, and you have a low AC target next to a high AC target, if you hit the low one, you can automatically damage the high AC one.  Of course, if you don't have a magical weapon, GFB is better due to ignoring non-magical weapon damage resistance, but not fire resistance.

Another point is what weapon;   A greataxe is 2d12 + 2xstat bonus if both hit in case 1, vs 1d12+1d8+stat bonus on a single target in case 2.

Single target, no cleaving, case 1 is better.   Cleave target, case 2 is better.  Again assuming you hit.

The math is different at higher levels, and based on class abilities selected it can vary quite a bit (like with battle master superiority die, certain smite spells, etc) and I am sure someone can point to the spreadsheet that outlines the damage cases.

Some other things to consider.

The two blade cantrips have a range of 5ft, even if you are wielding a reach weapon.

Unlike most attack spells, the blade cantrips can be used in darkness and silence. Situationally useful, but very useful in those situations.

The cantrips can be counterspelled. Attacking a target cannot.

Features like divine smite and spells like branding smite do work with the blade cantrips.

Personally, I feel the two blade cantrips are overpowered. The two casters in my game always use them because why wouldn't you? The cantrips have become a spell tax, in that if you don't take them then you are nerfing your character. It does require multiclassing for a paladin, I guess, but every paladin ever played in my games has been multiclassed.

Quote from Greenstone_Walker >>

 

Unlike most attack spells, the blade cantrips can be used in darkness and silence. Situationally useful, but very useful in those situations.

 

While you can cast Booming Blade under the effects of Silence it would be somewhat useless because things inside the Silence spell are immune to thunder damage. Though I suppose it would work if you are just inside the spell and your target is just outside.