First off, if you're new to the pen-and-paper D&D, 4E will be easier for you. Character creation is easier. There's even suggested starting builds for each class, which is handy if you just want to play right away and try out a character. Starting at level 1 is also more survivable. It's easier for the Dungeon Master (DM) too, since they've designed 4E to require less time to prepare combat encounters and provide appropriate loot and rewards to the players.
Secondly, there's a handful of improvements to 4E in terms of game mechanics. Every class now has powers, some of which are usable once per day, once per encounter or at will, depending on the strength of the power. This means that the non-spellcasting classes like the fighter and rogue are no longer hack-n-slash like in 3.5E. This also means that the spellcasting classes never run out of spells.
The healing system has been revised. Each player, regardless of class now has an ability to recover from damage every once in a while. It's still difficult to play without a healer, but unlike in 3.5E, they're not absolutely required for survival anymore.
A role system has also been implemented. Similar to some online games, there are now defenders (tank roles), controllers (crowd control), strikers (DPS), and leaders (support/healers). Unlike in 3.5E, there's now concrete reason for enemies to not ignore the fighter and just go for the squishy wizard, which makes more room for tactics.
So 4E looks bright and shiny, yet I still find that I miss some things from the 3.5 edition.
For example, critical hits. In 3.5E, scoring a critical hit is always an awesome moment, what with the multipliers and all the dice that you roll. In 4E, there is no confirming d20 roll for critical hits, and so it's also weaker in terms of damage. Sometimes you don't even roll damage dice at all.
Also, in 4E there is no longer a universal list of spells. Each spellcaster class has a unique set of spells. So if you're a wizard, you can never learn sorcerer spells. Also, schools of magic are no more -- no more specialization.
Spellcasting classes are no longer as awesome as in 3.5E. Sure, they had a limited number of spells and when it's all used they'd have to resort to crossbows or staves, but when they did cast spells, it was much more impressive and memorable.
Moreover, magical items are less powerful. In 4E the most powerful item abilities can only be used once per day, and a player has a limited number of times that he can use these magical item power.
Skills have also been simplified -- maybe oversimplified. You can no longer distribute points as you wish for a more customized feel -- now it's either you're trained in a skill or you're not.
So sure, 3.5E had lots of room for improvement, but so does 4E. Each design has its fine points, and also its accompanying flaws.
