Admittedly I never really take damage in R2 unless I'm either acting like an idiot or purposefully playing with the game's rules (like: you can only kill that Henchman with the powder keg right there, even though he will shoot it out of your hands and make it explode in your face about eight out of ten times) and I have taken some (dumb) damage in Rayman 3 in the past, but I'm going to go ahead and have that be a direct consequence of me playing R2 since I was maybe six or eightish and have played the game through at least ten times from start to end, while R3 I've only played, years apart, too, maybe four times in total (from start to end that is). That and R3 being a longer game in general puts the comparison in a bit of a skewed view.
However, what I wil say is this:
In Rayman 3, taking the Longest Shortcut as an example, the environment only rarely combats you directly. There's no way you get punished unless you happen to fall into the middle of a lava lake, which you then hop-skip across (wtf) until you get hit three times and somehow take exponentially more damage the third time, instantly killing you (even more wtf - if you're going to make lava-physics broken, don't make hem half-broken). There's not really any dangers in the game aside from carefully placed enemy encounters, which always seem to take place in harmless environments.
Now in Rayman 2, there's always something. There's lava, acid, deadly oil, Piranhas snapping at your feet, Baby Chenilles hungry for a piece of Rayman, Baby Janos that appear from underground and eat you alive, Nettles bursting out of nowhere to hit you smack in the face, all while you're most likely already occupied with doing something else. And then sometimes, in the middle of this, you need to quickly divert your attention to a Cage that you must also break before your window of opportunity closes on you (Nenuphar bit in the SoRaL).
While Rayman 2's mechanics allow for an easier execution (Rayman is a lot steadier and moves slower than in Rayman 3, where he's more acrobatic, falls faster and as a result makes his own movements a bit of an obstacle too), the premise of difficulty is far higher. And the game is designed for younger players, clearly, and as such the skill level required isn't anything that makes us go 'wow' at the age we are now, but I can distinctly remember times when I was stumped trying to get passed somewhere as a kid. There's this one part in the SoSaF where you're hopping down from a ride down the lava river and you land on a platform and all of a sudden there's Flame Caterpillars hunting you down. I've been knocked into the lava down from my platform a few times before. And the Prison Ship is one big obstacle course. Not only the enemies are your enemies. The environment is too. And that makes the game harder, given a certain skill level.
In Rayman 3, the punishment is nearly always backtracking. Take the Knaaren Desert. There's this part where you carry an egg over a floor of shoddy platforms. When you step on an unstable one, you fall through the floor and break the egg. You need to climb back up and start anew, but that's all the punishment you get. Oh, and Zombie Chickens roam down there, but they're not that hard to deal with. If you mess up in Beneath the SoRaL, you get to respawn right at the beginning of your course. Get your execution right, Rayman, or go back to spawn.
There is that part in the Tower of the Leptys where you need to get it right or respawn, but that's one of the only places I can think of.
Basically, in Rayman 3, you're always solving puzzles (which is fine, truly, I enjoy it a lot), be those time-based, combat-based or platforming-based, and in Rayman 2, you're trying to manoeuvre your way through a dangerous world teeming with fierce monsters. Rayman 3 starts your skill level slightly higher in the combat scenes compared to 2, but the platforming skills required of you are far, far lower down just because of the lack of harmful environments.
But that's just my thoughts on that matter. I know my arguments won't hold true for every section of either of the two games, but in general, that's what I've noticed.