Thank you for the detailed response. In the end, with limited mental bandwidth, it doesn't seem like there is any particular reason to learn Cortex Prime just to run (as an example) a Trek game, when I could just use Fate which I know pretty well.
I think it would probably be more helpful to look at a specific example, so you can see what it is doing that Fate does not. And I enjoy Fate, it also does thing Cortex doesn't.
Marvel Heroic Roleplay is actually Cortex Plus, which a half step back mechanically, but still a good example.
First, it's designed not to be a superhero game, it's designed to be a comic book game. What I mean by that is that it plays to a lot of the conceits of the comic book. One of the things that leaps out from the very top of any character sheet (called Datafile) is directly below their name is called Affiliations. Basically solo, buddy, and team, with a d6, d8 and d10 scattered among them. Because in comic books these are very often the split ups. Spider-man was always acquiring a buddy, and it's the whole idea behind Batman the Brave and the Bold, or just with Robin, while Captain America is a tactician who elevates any team they are on. These dice are added to every die pool.
Next is distictions, much like Fate Aspects. And like Aspects you can use the positively for a large bonus die, or negatively for a plot currency and a d4 bonus die, which is usually more harmful then helpful, especially with 1s advancing the Doom Pool.
Next you'll have one or two power sets. For example, Cap is both a Super Soldier and has a Vibranium Shield - these are separate power sets. You describe your fiction, and you can grab up to one entry from each power set that fits what you are doing. For example the Vibranium-Alloy Shield had d12 for Durability and a d8 as a weapon. It has two Special F/X (SFX) that are stunts you can do, like Ricochet and the rules for it, and it has a limit, that it is gear and be shutdown, for which you gain a plot currency. And how to recover it (take and action vs. the doom pool).
Again, you can be creative. Want to describe Spidey as taunting one villain to shooting at him, dodging, and that shot collapsing something on another villain? Go for it.
The last part of your dice pool you make is your specialties, which are basically like skills, training, knowledge, and contacts.
Just like Fate, there can be things from scenes and from your target that can affect your total. Damage especially. Unlike in Fate where you have one free tag, target damage adds dice to your pool whenever it would be appropriate. Damage is in three flavors, Physical, Mental and Emotional. It's basically the effect die (the size of the biggest die after you take out your dice to succeed or fail).
Mind you, Spider-man quipping (doing emotional damage) can be just as effective if not more than punching someone. Adding another type of damage means bonus dice in later pools, and any of the three types going past d12 can take someone out.
Play generally alternates between action scenes and transitional scenes. Transitional scenes give chances to recover some damage, create assets (in Fate it would be creating an Aspect like "Radio Tracker" or "Codebreaking Library" or "Tactical Intelligence", though with a die so it could be used in upcoming dice pools).