Both have strong points. I love Oblivion for it's custom spells, and simple joys such as naming enchanted items. Oblivion's DLCs were fantastic as well, Shivering Isles by itself would be an amazing game. As far as story both have strong and weak points, in general I prefer Oblivions guild quests. Skyrim over all is a better game however, a refined leveling system and the addition of being able to forge and craft your own weapons and armor is a huge plus. I also really enjoyed the lore of Skyrim, especially concerning the Dwemer and the Dragon Cult.
Skyrim. It's not even a contest. Oblivion is... honestly not a very good game. The combat is extremely monotonous and wannabe hardcore, the near impossibility of committing a crime without a guard instantly showing up WITH THEIR FACE RIGHT UP AGAINST THE SCREEN restricts freedom and is beyond annoying, the story is over-indulgent, the facial expressions and dialogue are laughable, and the level scaling is OMG WTF WHY ARE ENEMIES LEVELING TO MY EXACT SKILLS?!?!?! *ahem*
It's not a bad game, but it was an enormous step down from Morrowind and a blemish on the series' great name. Skyrim wasn't perfect, either, but it helped get the series back on track.
Skyrim, It was an excellent game and it's game world was truly beautiful. It fixed a lot of things that were wrong with oblivion such as repetitive dungeons, and some of the broken combat. I really did some the drawf (I forgot the names drawfs are called in the elderscrolls series) ruins too those were fantastic to look at. I also preferred that Skyrim had plenty of smaller settlements scattered around it's countryside, something that gave a lot of life to the land unlike oblivion which is a shame. Although Skyrim had some drawbacks such as smaller capital cities, which sadly had to be done for console players, as consoles wouldn't of been able to handle the size the cities were in oblivion with the updated graphics. I think Skyrim easily beats oblivion myself but hey that's just the core game, Mods are what really strive this series along in my opinion.
Oblivion. It was just sooo much more memorable to me! I have a ton of great memories playing Oblivion, and very few playing Skyrim. Skyrim is just... bland. It's snow snow snow everywhere, and the music is... forgetable honestly... Here, let me put two random tracks from each game side by side.
I don't know what it is, I just prefer Oblivion's music so much more. Like, Skyrim's music sounds good when you're listening to it, but you can't really hum it again later. Like I said - forgetable IMO.
I also thought the story was infinitely better in Oblivion. The Emperor has been killed, oh no! The Gray Fox, is he really just a legend? Who's the traitor in the Dark Brotherhood?! In Skyrim, aside from the main quest (which I'll admit was pretty good), the stories behind the Mage's Guild, Thieve's Guild, and Dark Brotherhood all sucked. I found TES IV way more immersive.
But I'll give Skyrim credit, the combat was a lot better than Oblivion's. However, I don't play an RPG for the combat. I may be a minority here, but I just really like stories and feeling apart of the world. And you may say Skyrim's graphics made you feel apart of the world, but honestly, I don't even give Skyrim the edge in terms of looks. It's bland. Boring. Oblivion's lushious greenery combined with its upbeat score is way more preferable.
And to be honest, I like getting in trouble with the law and having an Oblivion guard pop out of nowhere and say, "STOP! YOU VIOLATED THE LAW!" It's corny and reminds me why I cherished Oblivion so.