Skyrim > Oblivion (duh)
I'm just gonna put it out there. Skyrim is awesome.
As for why, well, that's a much longer statement.
This game does not need my praise as it's gotten overwhelming support from game critics and the community, but I'm gonna put my own two cents out there anyway.
To be upfront, I did not like Oblivion. Something about how that game began, the lack of direction, the clunkiness of the combat and the bugginess of the game engine put me off three separate times. Skyrim fixes a lot of those issues.
I feel the start of the game is stronger than Oblivion's (if you remove Sir Patrick Stewart from the equation)., in that it remains fast-moving and gives you a good primer on many of the systems (although some more explanation about magic and the favorites system would be nice). I found the town of Riverwood much more inviting than the monstrosity that is the Imperial City. My own personal preference of course.
Some people complain about the compass and the plot arrows, but I think they're a great addition from the Fallout series of games. They may make things a bit easier, but they just add to the wanderlust you get going through the immense world of Skyrim. Also, I don't know about other people, but I don't like to get lost, so having a convenient plot arrow is a bonus in my book.
To be honest... I can't really tell you what's different about Skyrim's combat from Oblivion's. It's still swinging a sword, backpedaling and blocking every now and then. Maybe the animations are smoother, or the timing is looser (or maybe it's just those awesome kill animations...), but I really do enjoy the combat in Skyrim. Not the game's strongest suit, but when has that ever been Bethesda's strong point? And it's definitely not a weak point in this game.
I am proud to say that Skyrim has only crashed on me thrice during my 80-odd hours of gameplay (apparently it didn't like a chest I looted and that I killed that Khajit). A massive improvement over Oblivion's constant instability. I can't speak to the graphical improvements, as I have it turned all the way down to the ass-end of the spectrum because my laptop is, well, a laptop. But the environment design is more varied than you'd expect from a winter-y continent and some of the dungeon designs are just flat out awesome.
I feel like I don't need to speak too much about the story, other than it's pretty sweet. The main questline takes you on a pretty good ride, although (and this isn't the point for the open world RPG) it felt a bit short to me. However, for everything else, Bethesda remains strong. I feel like every side quest is given just enough attention to make you feel like you're not doing yet another side quest for yet another sum of gold and XP.
Speaking of XP, the leveling system. Oblivion's leveling system was... weird. The scaling brought all sorts of craziness to your character's performance, which put off a lot of people, including me. Skyrim simplifies the leveling system a bit further than an RPG-geek like myself would have wanted, but I feel like I still have a good amount of control over the direction of where my character goes (except for leveling Restoration to 40 to get that damned perk...). Everything in it is fairly intuitive and almost every time you level up, I feel like you get a tangible benefit.
Oh, right, one more thing. The interface. It's obviously been designed from a console perspective, which would normally annoy me, but that also means almost every menu can be navigated through WASD and E, which I personally find a helluva lot more accurate than using a mouse pointer. Favorites are an interesting idea, if a bit hard to get used to. Reading the manual helps. Scrolling through items gets tedious at times, but something akin to that issue probably would remain regardless of the interface. The one complaint I do have (and this is horribly nitpicky) is that you should be able to select OK with E and not the mouse. Consistency, people.
All in all, again, Skyrim is awesome. It's the best game Bethesda's put out so far, and despite its few flaws, it remains an immensely enjoyable experience all the way through. (Just keep quicksaving!)