I encourage you to check out the post I linked above. I wrote it, specifically breaking down all the points of design where I felt the two games diverge despite appearing similar (and at least a few places where 5e is more like 4e than 3e!)
The one thing I didn't specifically discuss there was short rest abilities. The fact that 5e changed the short rest to be an entire hour pretty radically changed the nature of short-rest anything in 5e vs 4e. In 4e, short-rest abilities are reliable tools, something you can count on to have basically all the time--with short rests being only five minutes, it's hard but not impossible to enter a combat without all of your short-rest abilities at the ready. Not so with 5e, both intentionally and unintentionally: they very much intended short-rest abilities to be stretched out over 2, or even sometimes 3 combats. They also intended that players would get 2-3 short rests (average 2.5 or a little higher) per day, when in practice, most groups go for 1-2 per day (average 1.5 or a little lower). Short-rest classes were balanced for a playstyle that doesn't, generally speaking, actually happen. So, in both theory and practice, 5e short-rest abilities are a rare spice to be carefully rationed; 4e short-rest abilities are reliable tools meant to be deployed consistently. Again, a case of "vaguely similar, but shorn of critical parts."
That's part of what's going to change in 5.5e, by the by. Most classes that use short-rest things are going to be reworked so that they instead use some variation on the "proficiency bonus per long rest" system. I'm not sure how they intend to fix some of the bigger issue cases, like Battlemaster Fighters and Warlocks who are disproportionately punished by getting few short rests per day, but they'll almost certainly do something.
Maybe what bothers me about some of what Alexander calls disassociated mechanics is not just that they are abstracted but actually that it is somewhat difficult to reattach what happened in the game back to the fiction. So a mechanic that says, you can trip someone 4 times per day feels disassociated for me (why only 4 times?), whereas saying they have a 20% of tripping an opponent if they try seems more consistent within the fiction. Or, as I understand it, 13th age doesn't have rests; your abilities just reset after X number of encounters. How does one attach that to the fiction, even after the fact? So it kinda strikes me as the inverse of the OSR principle to not look at your character sheet, because in these instances the only way, it seems, that you would understand what's going on in the fiction is if you looked at your character sheet and saw, oh yes, this comes off cooldown now, or I've run out of uses for this ability.
Into the Odd is one game that made the equivalent of "short rests" make sense for me, because HP is "Hit Protection" and defined as your character's energy and ability to dodge and such, whereas the characters strength score can be damaged and that represents actual physical injury.