Shadowrun 4 uses a largely different mechanic from Shadowrun 3: SR4 uses the new World of Darkness dice mechanic rather than the classic Shadowrun mechanic (except they use d6 instead of d10, but 66.7% and 70% are basically the same probability...). The justification for the change was to speed up combat and other conflict resolution, which it does to some extent, by not having to keep track of both target number and number of successes (all target numbers are now 5; some things have thresholds for the number of successes you need--all the math is just done on # of successes). Also, dice pools are gone, so there are many fewer tactical decisions to make, also speeding up the process. (If you enjoyed selecting just how many combat pool you were going to use for soaking so you had enough left to take out your next opponent with one shot, you will be disappointed. If you were annoyed that you had all these extra decisions to make when you really just wanted to kill the bad guy as quickly and effectively as possible, you will be pleased.)

Because of the drastic change to mechanics, SR4 is a dramatically less versatile system; it works with a much narrower range of abilities and difficulties. On the other hand, the game has been balanced so that a normal run will be right in the middle of the sweet spot where the outcomes in SR4 do not feel drastically different from SR3. So if you were doing standard runs before, and will be again, you can take advantage of the simpler mechanics without much loss. SR4 breaks badly as characters or NPCs become extremely powerful (e.g. you need an impossible number of successes to defeat them, with d20-style "I stand in the middle of a room full of goblins for hours and they can't hit me" scenarios), so there are various caps and limits that were much softer before; starting out, you can make a runner who comes pretty close to the best in the world in something. Whether you like that or not is personal taste, but it is definitely a difference.

Anyway, the take-home message is that you should be prepared to feel like you're playing with different mechanics. The same concepts are mostly there in some guise, but it scarcely would have been more different if they had switched to d20.

Despite the mechanics changes, the setting feels much the same as before. Otaku are now Technomancers, and the old separate-worlds idea of the matrix has been replaced by a parallel augmented reality version that greatly helps with integrating deckers (now hackers--no more decks!) into the flow of gameplay. The timeline has advanced another decade or so, but aside from the crash of the old Matrix and replacement with the new augmented reality stuff, there's nothing that will radically change how your character approaches the world. The new mechanics are balanced to yield similar outcomes for standard runs, so you'll be approximately equally worried about a team of security guards or whatnot; if you were using SR3 the way you were "supposed" to be, you'll mostly just notice that SR4 runs a bit faster and that you can see your decker face-to-face.

The major changes I noticed between the two editions are as follows:

Limits prevent characters from being overly min-maxed. Each of them is centered around an attribute that is typically dumped in normal characters; the most important attribute for the physical limit, for instance, is Strength, though other attributes weigh in they have the same impact as Strength does alone. This means that you can't build a "never gonna fight close quarters" build and just dump strength and expect to do well in other physical areas, encouraging a well-rounded thing.

Mystic adepts get a huge buff. I'm not exactly sure that this is a bad thing; they still can't astrally project, but they get the powers of both mages (other than astral) and phys-ads pretty nicely. Were they still using the BP system, this would be a flaw, and I'm not sure about allowing them as the third pick on your priority system, but I think the reason that people are upset is because they don't astrally project as much as they should when not a mystic adept.

The priority system really makes things a lot better. It prevents some of the worst cheesing during character creation (don't get me wrong-it's still possible, but you have to know what you're doing and make some sacrifices).

Combat's been changed rather heavily on the bookkeeping, but not so much the execution. The Accuracy limit keeps pistols from killing Great Dragons, which is a nice touch, but also discourages just dumping into the newly increased skills and maxing them out right away. It also makes smartlinks a more tangible advantage, as do laser sights. Armor is now a single rating for stun and physical, which makes it a lot easier for new players to understand, and, in my opinion, more realistic.

Hacking's a lot better. Mind you; the wireless thing contains some logic holes and gimmicks with the new benefits it gives stuff like cyberware or laser sights, but hackers can enjoy a target rich playground with new rules for hacking that make prepping a hacker 90% easier and playing one about 50% easier; GM'ing hacking also became a lot easier. In addition, some of the more broken technomancer stuff has been revised so you now have a reason to play a decker instead of a technomancer every single time.

All in all, it's faster and more streamlined. If you want my "reviewer" version, you can check it out on my blog, but I've said pretty much everything I said there here, only without the sales pitches.