It's been a long time since I've played either, but I think my main reasons for liking Oblivion more were that I thought it looked better than Skyrim, not technically but artistically. Skyrim is one of the most drab fucking games I have ever played. The variety of enemies in Skyrim is pretty lacking. I only remember fighting people, zombies, spiders, lichs, dragons, and robots. Oblivion kind makes it hard to see all of it's enemies with the shitty level scaling, but at least they were there.
Then the biggest difference would be the quests. I played nearly 100 hours of Skyrim, and nearly every fucking quest amounted to "go to X get Y, and kill Z if you see him." Even the guilds, which had some of the best quests in Oblivion, were fucking ass in comparison. ESPECIALLY the Dark Brotherhood quests.
I think there were some other things too, but I haven't played Skyrim since the year it came out and I haven't played Oblivion seriously since even before that, so I can't really remember anything much more specific.