*Before going any further, this will have spoilers from both games*
Anyway, lets get straight to it, I think, that Oblivion had better quests, starting with guild ones, they were so much more fleshed out, and IMO better jobs, like the thieves guild, on Oblivion, it involves stealing lots of things (Duh), and you got some pretty epic missions, like stealing an Elder scroll, on Skyrim, it has become the nightingale questline, nothing to do with stealing, just hack and slash dungeon crawling, now the fighters guild on Oblivion to most, was just a dungeon crawler boring group, but I found their quests interesting, there was a good plot twist near the end, and the whole feud with the other mercenary group was quite good. But the Companions... god I don't like these guys, lets see, you get attacked by this werewolf hunter group called the 'Silver Hand', and then you go hunting them down murdering them like crazy, and we don't even know anything about them! They are just "The bad guys". Also, the storyline cannot focus on one thing, it is constantly jumping from fighting Silver Hand, to curing Lycanthropy, what happened to the silver hand? Are they still there? What are their motives? The mages guild on Oblivion was pretty straightforward, not much to say about that, the College of Winterhold had a few things I didn't like, such as wasting such a good character, the High Elf bad guy (Forgot his name) was kind of wasted IMO, it would have been a nice touch if the arch mage was actually the bad guy, and then you have to work with the guy. And you see at the end of the questline, ,the monks come in and take the Eye of Magnus away, just like that, well, why didn't they do that earlier? Why go through all the trouble? The Dark brotherhood I preferred on Oblivion, but it was okay on Skyrim. The Bards College was a HUGE disappointment, they could have done so much with it, like somebody mentioned, it could have actually been a spying group, it would have been a group focused around dialogue, and convincing other people to do stuff, sadly, it was a handful of meh quests.
COMBAT
Now, the thing is, on Skyrim, combat feels a bit, dumbed down, it's like you sit there and shield bash a guy then whack whack whack, shield bash, if playing on a harder difficulty, you have to use the stun moves loads, otherwise you get murdered. The combat is also very clunky, lots of the time Shouts don't shout when their suppose to, lots of recharge problems. I do like the implementation of duel wielding though, good idea, pretty well done. Then there is destruction magic, which is very weak on Skyrim, the problem is, most of the big damaging spells, take loads of magic, and do, say 70 damage, and the thing is, whacking somebody with a sword does 60 damage, yet has no limit! and is also faster, and most of the time, the melee weapons out damage magic. This is why hitting took Fatigue on Oblivion, so that you couldn't just keep whacking for ever and doing tons of damage. also, the magic on Oblivion took a whole lot of magicka, yet it packed a punch, if you were playing on a higher difficulty, you needed to make yourself a powerful spell to get through some places. (Spell creation taken out of Skyrim is a bit annoying too.) And then, on Oblivion, there was Athletics and Acrobatics, Athletics really helped in Combat on Oblivion, instead of standing still whacking each other shield bashing, most of the time you would be dodging, it would be very hectic, and a lot more fun.
MAIN STORYLINE
Now, Skyrim's main story, IMO was a bit lacking, the thing is, Alduin has no plan, sure he wants to take over, he sends out Dragons, hooray! But for what? What is he trying to do? What is his grand plan? Nothing. there was nothing obligating you to kill Alduin fast, like, do this or Alduin will destroy the world, he just sat around summoning Dragons.On Oblivion, Mehrunes Dagon was making more and more Oblivion Gates, getting him closer and closer to Tamriel, letting him invade full force onto the land, this was actually a problem, Alduin did nothing. And then, there is how dragons are displayed, they are supposed to be Powerful, yet they cannot even use their own shouts! The shouts you gain are more suited for humans than dragons. Then, there is the whole two Dragonborns business (I really liked the Dragonborn DLC main story) which just makes them look weaker, Mirak has killed many many Dragons, and can summon them to do his bidding, as if they are his slaves, Dragons were not portrayed too strong there.
World
I felt Skyrim was kind of the same thing, there was tundra, and snow, that's it, nothing different, but Oblivion, had so many different things, there was the gold Coast, The whole snowy area near Bruma, Swampy arena near Leyawiin.
/End Rant.
Thank you for reading, I am open to discuss any of my points. (I will not discuss graphics here, they make up a very small part in my opinion.)