One big difference is that the GM (or the rules themselves) aren't pre-defining your aspects for you. So by choosing your aspects, you're choosing what kinds of conflicts or troubles you want to have. Basically, when you put down an aspect, you're signing up for it to be compelled. (Although certainly some aspects are far more compellable than others, which some players also use when constructing their characters.) In this way, the GM isn't really demanding you act according to his dictates, but pushing the character to act as the player stated it would (or sometimes, pushing for the world to react to your character the way you said it would). The nature of the aspects is always in the hands of the players. Additionally, since aspects are defined in a freeform way, your aspects can be as specific and detailed as you see fit. There can be tremendous mechanical variety to characters in Fate who might all be "paladins" under a D&D scheme.
But your aspects are limited by genre, who your character is, setting, etc... so to a point they are pre-defined. You aren't going to have an aspect like "uncontrollable magic power" if your GM is running a grim and gritty game in a cyberpunk setting, because it doesn't fit the setting. You also choose your class, race, alignment, etc. in D&D and through choosing these things (since these choices are not pre-defined for your character either) you are choosing the kinds of conflict and troubles you want to have... You don't play a character class bound by moral rules if you want the freedom to act in any way you see fit... Just like you wouldn't pick an aspect like "Thrill Seeker" and spend the majority of the game scared to act.
Also, when you choose to play a character who has powers based on alignment, you're signing up for having to abide by the GM's interpretation of that alignment (just as a DM decides in Fate whether an aspect can or cannot be invoked, compelled, etc. in a certain way...). The DM isn't demanding you act a certain way with alignment either according to how you phrased it above... but pushing you to act the way you said you would when you picked that alignment and/or a certain character class...
Speaking to mechanical variety as far as paladins go, especially since in D&D a paladin is a specific class and in fate it's a descriptor... that's comparing apples and oranges... I'm also not sure how much mechanical variety there is in a fate paladin since it's pretty specific as far as what aspects actually do... (+2 to a skill roll, +2 to a friend's roll, +2 to a passive source of opposition, or reroll your dice). I'm not seeing much variety here, in fact it seems downright anemic compared with what going to level 20 in the D&D paladin class of almost any edition gives you.
As for the punishment angle...Fate points are more of an economy during play, rather than finite resource. You should be anticipating such things coming (and going), and Fate points don't usually get treated as a rare resource. While I suppose you are technically correct, it usually doesn't feel that way, IME. In Fate, if you find yourself running out of Fate Points, its usually a sign that the character isn't working the way you intended it, or it isn't striking the interest of the rest of the group. Additionally, you're character never stops being <whatever> merely on the whim of the GM. That is, you may have to pay a Fate point for it, and if it happens a few times you might want to reconsider the problematic aspects, but the GM can't suddenly declare that two of your aspects just don't work and your stunts are all gone.
Can you invoke your "paladin" aspect without a fate point? If not then sooner or later the GM will dictate what you should do if you want to retain the ability to be a paladin in Fate. If you loose a point every time you resist a compel, and by default the most Fate points you can start out with is 3 (though if you want an extra stunt or two that drops it to 2 or 1) it seems like it's just a more obfuscated way of making it so that the GM can enforce "good play" on your part... Especially since as per Fate Core the GM is the final arbiter on invokes, compels, etc. I don't see much of a difference between a GM controlling through alignment penalties or through resource economy when they are both basically up to the judgement of the GM.
Now, IME, declining a compel rarely happens, and when it does its usually perceived as an invitation for the GM to come up with something more interesting (although the GM can also up his offer to 2 FP). I can't say if that's a universal thing with Fate or not, but it seems common, at least.
So basically most of the time the player is going along with how the GM feels they should be playing their character and gets rewarded for it (Yet for some reason they chafe when expected to do the same thing in D&D???)... I understand because I wouldn't want to run out of Fate points either and not be able to use my paladin aspect... the same way I wouldn't want to fall in D&D and loose my paladin's powers.
