In addition to the various other things mentioned, I think the TOS films handled the ageing thing much better than the TNG ones did. The fact they're getting older is acknowledged, they don't just stay in the same job for two decades (the short in fiction gap between four and five is the only time the status quo is really maintained, the rest of the time there's a sense they're off living their lives and all doing different things on and off with not everyone staying on the Enterprise all the time).
There's also a general sensible lack of physical action, and what we do get is either played for laughs (Kirk vs. Kirk or the rock climbing) or has the character at a disadvantage (Kirk only beats Kurge because the planet is exploding around them, and Sybok uses him like a rag doll). About the only serious physical feat in all six films is Kirk and McCoy's march across the ice in VI, and that really hurts McCoy.
In comparison, the TNG films don't change, evolve or age the characters at all. Even with Data's emotion chip, the one big change, that winds up being seen as such a failure it's forgotten by the final film. They just sit in the same chairs doing the same jobs for 15 years with little sign of anything going on in their lives beyond that (Worf's tenure on DS9 was not only down to outside constraints but had no impact on those two films after his introductory scenes, he might as well have been on the Enterprise all along,. strange they never thought of giving him a subplot where he has to work with the Enterprise's security chief).
And as they get older you need more and more suspension of disbelieve over the increasingly over the top action scenes. Everyone in Nemesis
is younger than the cast of TUC, but Picard and Riker especially look much more worn out and tired than any of Kirk's crew do because we're supposed to try and buy them as being capable of killing an entire bridge crew of Remans alone or beating the shit out of Ron Pearlman. it just looks... silly. In a movie that's trying to be very serious.
One thing I've always found interesting is how FC really does feel the most cinematic of the TNG movies (though I'd agree with the above that the others aren't that
TV like despite their other flaws), but the story is most like that of a TV episode with it's clearly defined and mostly seperate A and B plots. But then, that's a film where objectively I can point at all sorts of things in it and go "That's crap" (Hello Borg Queen) but when watching it I manage to get completely caught up in it and enjoy in immensity despite the logic flaws. Which I suppose, is what a good big dumb action film will do.