(I don't mean all of Uru failed. Just those puzzles to which 3D movement and physics were integral. Nice ideas, unfun in practice.)
I am now going to try to analyze why Tomb Raider: Legend pretty much gets it right.
First let me sketch out the game. Tomb Raider is mostly environment puzzles: the kind of jumping, climbing, rope-and-ledge exploration which made the franchise famous in the first place. (A younger gamer than me would call them Prince of Persia game elements, and then I would mutter maledictions into my hoary beard.) This stuff is broken up by gunfights (pleasantly easy, even for me) and by physics puzzles.
How am I distinguishing (old-style, jumpy-climby) "environmental" puzzles from (exciting-new, spatial) "physics" puzzles? The old stuff applied laws of physics (or at least good preprogrammed approximations) to the protagonist's body. The environment was either static, or set up with pre-programmed reactions. The new stuff does all that, and also applies laws of physics to parts of the environment.
So you have a crate, and you can drag it around. But not by pushing it in one of four directions (the cellular automaton crate puzzles that we know and dread). You can drag it at any angle; it swings ponderously around and follows you. If it hits the edge of a ramp, it angles up. If one corner hangs up on another crate, they both move -- half as fast, and maybe at different angles, because of the centers of gravity. You know: physics.
Now, crates are not surprising; I'm sure plenty of high-tech shooters have had crate physics. What Tomb Raider does is to line up the physical effects and design puzzles around them. It's nearly encyclopedic. Crates. Crates on a see-saw. Balances. Balances with moveable weights. Pendulums. Pendulums that bump things. Floating blocks. Floating blocks that you stand on. Floating blocks that bump into each other. Floating blocks that you pull with your grapple line. Floating blocks that you stand on and pull by shooting an anchor with your grapple line. I'm not listing every puzzle, you understand, just some highlights.
Why do these puzzles succeed, when Uru didn't so much? Well, a couple of straightforward reasons. Tomb Raider has a longer list of basic commands. You can grab crates; you can fire a magnetic grapple. (Uru didn't let you grab anything.) Tomb Raider happily sacrifices realism to invent useful game mechanics: only a few objects are grapple-able (and those have a distinctive magical shine). Great for puzzle construction; not so great for mimesis.
Also, to be honest, Tomb Raider is aiming lower. The puzzles are common tropes: drag the gold cube onto the gold plate. Turn the wheel (because Mr Headphones Dude tells you it needs turning). Pull the platform to where you can jump on it. You are not, for the most part, figuring out the habits of magical alien fireflies or messing with mechanisms that open one door while closing two. The puzzles in Tomb Raider have state, but not confusingly interrelated state (as Myst puzzles tend to have).
This is not to say that Tomb Raider is simplistic. It has lots of these common tropes; each game mechanic has lots of variations. And completeness forms its own kind of complexity. Just because you recognize the principle ("that thing swings") doesn't mean you see where to swing it. At the same time, the more experience you gain, the easier it is to think of new experiments to try. This is a basic adventure-design principle (which, of course, the environmental puzzles have been exploiting since the first Tomb Raider). A group of related puzzles, of increasing complexity, will engage the player better and occupy him longer than one blazingly difficult puzzle which stands alone.
(In fact, prospective imitators -- and sequel-writers -- are in trouble. I think this game has mapped out a majority of the possible things you can do with these physical elements. Go ahead, prove me wrong...)
But Tomb Raider also succeeds in a couple of more subtle ways. Remember I said the puzzles had state? All the positions (and rotations) are continuous -- unconfined to any grid. But you can still consider each puzzle to have definite states: the crate is on this platform, the platform is over there, the raft is in that room. Figuring out the important states is, of course, part of the puzzle.
What Uru did wrong, in that damn walking-over-the-baskets puzzle, was to glory too much in the wonderful rolling irregular baskets. There was no state you could get them into where you could say, fine, that's where I want them -- and then stop worrying. The more-or-less-right arrangement you wanted was fuzzily defined, hard to approximate, and easy to screw up.
In contrast, Tomb Raider's states are fairly sharp-edged; and once I got something set up, I rarely knocked it apart by accident. Yes, these "states" are emergent effects. It's possible for a crate to be half-off a platform, or for a raft to get hung up on the entrance to a new area. But those intermediate states are narrow and unstable. They're not swamps that you struggle to get out of.
Another trick, which you may never notice because it's done perfectly: you can't get stuck. Physics puzzles are horribly prone to irreversible mistakes, because physics is full of irreversible effects. Knock an object off a cliff, and it's gone. Push something into a pit, and if it's too heavy to lift, it's staying down there. Furthermore, when the simulation is so detailed, there are lots of ways of knocking things off cliffs. Possibly more than the designers anticipated.
I'm not positive that Tomb Raider is free of fatal physics mistakes, but I didn't run into any. I saw a couple of spots that might be potential ones -- but I would have had to work hard to test them. So you can play with toys, but you probably won't break them. Which is not an easy thing to arrange.
(In fact I did manage to get stuck at one point, but it wasn't related to a physics puzzle. It was a good old-fashioned climbing puzzle bug. I fell somewhere I shouldn't have, and the fall didn't kill me -- as it should have -- so I had no way back. Annoying, but not related to my current thesis.)
Let me jump briefly to a completely different game mechanic. Tomb Raider has a few action sequences which are (is there a common term for these? guess I'll invent one) prompted cut scenes. Time slows down in the middle of an exciting move. Something is coming at you (or you are flying at something). And, pop, a controller symbol appears: hit square! If you do, you live. If you don't -- or if you take too long -- you die. The scene has three or four of these in a row, and then (whew) you're back on stable ground.
So this is a familiar idea; it's straight out of God of War, which stole it from, heck, from Dragon's Lair. But it's worth noting a new twist: the buttons you have to hit are semantically meaningful. X is jump; circle is duck; square is the grappling line; and so on. (Same controls as in regular gameplay.) The animations are constructed so that you can see what's going to happen. You can react to the world, as opposed to the symbol. Which makes this an adventure element, in a way that God of War's button sequences were not.
I don't mean that it's a pure adventure element. If you screw up, you have to start the animation over, and the sequence is the same each time. So of course it gets mechanical very quickly. By the third try, you're not thinking "jump, duck, climb" but merely "X, circle, joystick". Nonetheless, it's a nice trick, and future games may be able to improve it.
In summary... Wait, you wanted a game review? I thought you were here for the puzzle design lecture. If this were a game review, I would be talking about all of the game elements: the good stuff (lots of side bonus quests, interesting boss fights, a time-travel story idea that doesn't choke itself to death) and the bad stuff (the game is quite short, and those motorcycle races go on five times as long as they ought). But I will happily recommend Tomb Raider: Legend, and I hope the development team (did I mention they're the Soul Reaver crew?) makes more of them.