I think that's because it's really not about the system, but rather about the themes/stories you want from that.. system.
I would start discharging the game system and analizing the setting/color, then working out how to model those with Fate.

For example, D&D isn't about the vancian magic in itself, as much as how magic impacts the fictional world and the stories you'll tell in there.

Something like: try to imagine the movie/novel you'd like to tell in that world. Then work your Fate hack from there.

Fate is very story focused, which makes fiction simple to emulate.

As +Nicola Urbinati said, other games core activity or main dramatic tension is buried under the rules intended to make it happen, so you have to search a lot harder. I'd start (and have started, for a Traveller conversion) with considering the "elevator pitch" for the game. How would you complete, as briefly as possible and in under 15 seconds, the sentence "[Game] is a game about..."

For Traveller, my answer would have been something like "Traveller is a game about traders and mercenaries adventuring to pay the bills in a young interstellar, interspecies trade empire with slow communications." D&D might be "... a game about high fantasy adventure in a Tolkeinesque world with elves, orcs, and dragons, where magic and divine power don't necessarily trump a ready sword arm." Those summaries, in turn, help you focus on what's important enough to try to replicate (alien species or magic items) and what can just be hand waived (ship design rules or monster threat ratings).

Oh, I get why it is. And, +Nicola Urbinati, that's exactly what I recommend people - my most common example is "Tomb of Horrors in Fate would be more like Tomb of Horrors: The Movie: The RPG than anything."

I just thought it was interesting, mostly from the POV of how hard it often is to mechanically translate other systems to Fate.

Aspects, not Abilities.

I was chatting with a friend the other day, and he said his group, new to Fate, was having some issues with understanding what their characters could do. They're doing Shadowrun which we've done since secondary school, so none of the game world is brand new. Nonetheless, for some reason, not having Firearms 5 or Hacking 6 written on their sheets was giving them trouble in figuring out what they were capable of.

You're the hacker? Of course you're a wizz with the tech gear! Stand-up shoot-out? Leave that to the sam and the physad who treats life like a vintage Western.

The thought I took away from it was that Fate lets you write your own permissions for your characters, whereas D&D and Vampire (etc) have you ask permission from the book.

But wouldn't they have those skills?

Or were they playing FAE?

They were, but considering the move to regular Fate.