As a lot of people have said, they play very differently. Personally, I wouldn't go so far as to say one is really better than the other, as they both have their fair share of problems (or elements that could be seen as cumbersome or unnecessary or something like that; I'm aware that one person's useless skill is another's priceless tactic).
I was torn initially about the changes in the skill system, but on the whole I like 4e's system a little better. It feels more streamlined, and it never made a lot of sense in most campaigns for there to be so many different skills. Sure, Concentration was an interesting mechanic, and there were some skills I was sorry to see go, but...Use Rope was annoying, as was Use Magic Device ("You mean I fought those dragons to get the MacGuffin and now I can't even use it!") and, well, I never thought it was particularly necessary for Hide and Move Silently to be two different skills. I mean, yes, they're two different skills in the most literal sense, but two different checks made being stealthy cumbersome.
4th edition also does a better job of balancing the classes (as others have said), which is sort of good and sort of not. On one hand, it sucked to be a 1st level wizard in 3.5; while your fighter and ranger buddies were on the front lines, hacking away every turn, you and your 4 hit points could cast four spells per day, and the most powerful one was probably Color Spray. But at higher levels, wizardly types quickly became more powerful than their "same level" martial comrades. So, yes, it's nice having some more balance that comes with the "powers" system. Everyone certainly feels like they're contributing in the campaign I'm in. On the other hand...does it really make sense for a 20th level fighter to have the same destructive power as a 20th level wizard? The fighter is just really, really good at shooting/stabbing/hacking/smashing things, while the wizard is a master of time and space, capable of doing almost literally whatever he wants (for a price).
I guess what the long wall of text is trying to get to is that 4th ed. feels more like a videogame in some ways, while 3.5 was more like an actual world. The rules and powers in particular seem less conducive to the crazy-awesome problem solving you might hear about from 3.5. Rituals are all well and good, but they don't fit well into the flow of the game, and I can't see anyone taking some of the old utilitarian spells (like Wood to Stone) from 3.5 as powers. In a group with newbies in it, plaing 4th ed. is fun because they can generally learn it on the fly, but I would prefer to stick with 3.5 for experienced players.