The modern controls are supposed to be better, but they are actually even worse because they redirect your guns while you are trying to dodge enemies, making it very hard to hit them consistently. Platforming isn't made easier by the modern controls either, the only benefit you really get from them is when you are doing nothing more than running around. So your best option is to accept that you need to get used to the clunky tank controls.
The first five games were made like that and it wasn't really until the sixth game (the first one on the PS2) that heavy criticism followed because Lara Croft didn't make a proper jump to the next generation back then. This is what triggered the decision for the first reboot of the series which baked in Ubisoft's Prince of Persia platforming from the Sands of Time trilogy along with modern controls. Tomb Raider Legend and onwards is when things got legitimately good. Lara Croft's early era is much like the original Crash Bandicoot game on the PS1: A lot of hype and fandom, but utterly mediocre with plenty of bad control and level design decisions that undo the good moments.
I played the first Tomb Raider before I had ever touched an N64 game. Even before the revelation of Super Mario 64, Tomb Raider felt like garbage. Its draw was that it was among the first 3D action-adventure games, but moreso than that, it had Lara Croft who became more popular than the games themselves.
Legend11 correctly predicted that GTA IV will outsell Super Smash Bros. Brawl. I was wrong.