Visually, TR4 is way superior, with better models and also better ambiance (mostly helped by better models). Even if all of TR4 is one area (Egypt), there was enough variation in the levels that it didn't felt stale too much. Also it looked cleaner, with no visible joints between textures, no object appearing through textures and much better draw distance. The walls of pulsating flesh and skinned monsters in the last levels of TR1 were slightly horrifying. TR4 did also a little in the horror registry, but differently, more with ambiance.
Basic enemies in TR1 feels less like bullet sponge, especially since human opponents are a minority, compared to TR4. Having a wide variety of animals (including dinos) to slaughter is fun. And fighting only few humans make each fight more memorable, compared to TR4, where the human enemies are nearly just as bullet-spongy, but way more numerous. At least the bigger weapon variety alleviate some of that issue in TR4 (explosive weapons FTW).
Levels seemed more impressive in TR1, but more linear and less maze-like (which I prefer to the more open/hub-like levels of TR4).
Gameplay mechanics: I'd say it hasn't changed much, with a slight advantage for TR4, as it seems slightly more fluid. Note that played both with the keyboard only, I successfully plugged my gamepad for TR4, but it felt much worse.
Except for the ability to crawl, which doesn't bring much to the gameplay and is way too slow, especially since it nearly always end up with having to do a U-turn at the end, which is slowwwww. And those passages are like everywhere.
Jumps seems a little more forgiving in TR4, with a shorter run-up. I'd also found that lateral jumps (to avoid enemy attacks) is easier to execute in TR4, due to (I think) different timings. I would have liked a tutorial (for example to learn that while walking you can't fall from a platform
) in TR4, but since it's the third sequel, it's not surprising they didn't bother. And vehicle phases don't bring anything really interesting, the controls aren't fluid enough and the physics too bumpy. Also the angle of the camera in TR1 has a few issues, with times where I couldn't see where I'm going to walk, usually in downward slope or stairs; I don't know if TR4 changed the angle of the camera or took care in the level design to avoid places with that issue.
I didn't have to consult a walkthrough as often in TR1, I think TR1 is easier than TR4, but I could also be getting better at this (yeah, in my dreams).