the lucky equivalent is fortunate. basically the only difference is that you can't use it on a roll where you have disadvantage, which...seems to defeat the entire purpose of the name of the feat while not doing a lot to nerf it.
The description is quite different:
"You gain 3 fate points. Whenever you make an attack roll, ability check, or saving throw and do not have disadvantage, you may spend a fate point to roll an additional d20 and choose whichever result you wish. You may do this after the initial roll has occurred, but before the outcome is known. If you have disadvantage, you may instead spend a fate point to choose one of the d20 rolls and reroll it. Alternatively, when you are attacked, you may choose to spend a fate point to force the attacking creature to reroll the attack. The creature resolves the attack with the result you choose"
So you can use the feat with disadvantage, it just works differently (you can reroll the worst result of a disadvantage roll)
the gwm equivalent is powerful attacker. it gives you a free maneuver you can use for no exertion which basically fulfills the purpose of the first bullet point of gwm, and the +10 to damage attack can be used with any two handed or versatile melee weapon and only imparts disadvantage - but not ALWAYS disadvantage, which means you can negate it with advantage, which means it's unironically even more busted then regular gwm.
Again, the description says something different
" Before you make a melee attack with a two-handed weapon or versatile weapon wielded with two hands, if you are proficient with the weapon and do not have disadvantage you can declare a powerful attack. A powerful attack has disadvantage, but on a hit deals 10 extra damage"
Which means that if you already have disadvantage you cannot just declare a powerful attack for +10 damage. It has to be a willing sacrifice.
EDIT: by how it's written, if your initial attack does not have disadvantage and you decide to make a powerful attack, you attack with disadvantage. You would not benefit from advantage given by other sources (this is how I'd rule it)