Tomb Raider just has better, immensely more satisfying combat mechanics. Even if the upgrade system was shoe-horned in and kind of worthless, at least you have lots of cool ways to mix up the combat. In Uncharted, you have guns and grenades. Lara also has that cool little dodge move.
That's just mechanics alone, though. There are plenty of other things that Uncharted does better than Tomb Raider, but it just doesn't "feel" great to shoot people. And that's mostly what you do in the game.
I've only played Uncharted 2 and Tomb Raider, but in asking what would make U2 better than U3 aside from thematic elements...well, encounter design.
From all accounts, ND added in the more complex melee system, so they felt they had to change the enemy and encounter design to facilitate that system. It threw off the very basic structure that U2 had and apparently caused numerous problems with enemies bum rushing you and throwing off previously successful strategies.
U2 was at its best when it motivated the player to utilize the more varied environment and progress through a space to gain an advantage. It was at its weakest when it encouraged a player to stick behind one box and play whack-a-mole at enemies at a distance.
No, wait, scratch that...U2 was at its absolute worst when it threw enemies with exceptionally high health and lethality and very few opportune moments to fight back. Running in circles waiting for the split second you could counter attack was frustrating. I almost thought the game had glitched when I fought the monster for the first time and he wouldn't go down after so many shots (without the super gun).
U3 seemed to add more of the moments...bullet sponge enemies while leaving Drake fragile. Add that to a melee system that, by the nature of its additional complexity and marketing hype, encouraged you to use it, only to get snuffed from the various enemies around because the animations take so long.
Tomb Raider, for all its Uncharted-like automation, added air control and an incredibly slick auto-cover system (which has been one of the few cover systems in a game that never killed me for being too sticky), which improved on the formula. The encounter design generally stayed in a cone of enemies in front of you, so while it lacked the motivation to utilize the environment to your advantage (at least on lower difficulties), it rarely had the portions that felt tedious or unfair. Lara also didn't have quite as much animation lag as Drake does, so the swimmy feeling in the direct movement was mitigated. You could get away faster when closed in on.
E and think the shooting mechanics in those games isn't the absolute pinnacle of the genre
