I think it's mostly visual and some control issues that make FFVII age badly. Otherwise though, I don't think there are very many RPGs that really do age badly once you're out of the 16-bit era, and quite a few of those (notably FF titles!) aged very well too. Admittedly I don't doubt that the age you got into some games can be a factor, but there's less you can improve on RPGs from the technology of the late 90s versus FPSes (on consoles anyway) and other more actiony games.
Random encounters are always something that could be done away with.
That said, FFVII felt like FFs V & VI but less. Same idea that the first half of the game builds the world while you're taking the tour on the rails, then the second half opens up due to shit hitting the fan and its side quest city while backtracking to see how everything's changed thanks to the big event. FFV had the worlds FU-SION-HA!, FFVI had the overworld reshaped to the point of nearly being unrecognizable, FFVII had a change in overworld music and a bright red splotch up in the sky. FFVI also has more characters and have the cast shuffle around more during the pre-shitty fan part while FFVII was more like "Alright _______. Time to force yourself into the party for your character development in this next area." or more precisely less subtle character development (it also didn't help that VII forced you to have only 3 party members active at once (but then again, outside of IX there hasn't been a four member party since)). Summon cutscenes started into their infamous cutscene showboating (the worst of this was Bahamut ZERO). And most of this was either overlooked or accepted at the time due to the shininess of the then brand new 3D. Now it just feels like an SuperNES era JRPG, but less, and with blocky Popeye characters on prerendered .JPEGs.
On the plus side FFVII is still vastly more playable than FFVIII is with its constant camera wigouts and showboating character animations per battle, drawing magic/playing Triple Triad until the cows come home, ridiculously overlong unskipable summon animations, and shallow, all over the fucking place, plot.