I really can't compare the two. Skyrim just seems like the next Oblivion, and both are equally great in my opinion. Oblivion was my first ES game so of course there is some nostalgia, and I find myself wishing to see some of the Oblivion cities with updated graphics, etc. But I do love Skyrim, and I love the story of Skyrim more than Oblivion's. I guess you can nitpick about the small details that makes one better than the other, but as an overall picture, they're the same to me, two great games.
Agreed. Adding: the two things which I think makes Oblivion more "superior" to Skyrim are
1) the larger cities and dungeons. The surface city areas in the Cyrodill land mass was HUGE. The population density was far greater. But that was because of the TES story line and era (Oblivion was the TES era that represented the height of Imperial culture and influence). This more than doubled the areas for exploration compared to Skyrim.
In Skyrim, the Empire is in decline, and the Imperial technology/culture which made the high density populations of Cyrodil plausible are abesent in Nord culture. The anology is how Ancient Rome had population density on the order of a millon, compared to the largest barbarian town (like the Gauls/Visgoths etc) which numbered less than 100 souls. The inhospitable climate also plays a big factor in population control in Skyrim. So the sparse populations in the even sparser towns and major holds reflect that.
Like Oblivion, you can also free roam in Skyrim--but a lot of the open sandbox/non questing game play has been now limited to random world/in town encouters. In Oblivion, you could spend hours ransacking NPC homes all across Cyrodill---regarless of whether you were in the TG or not---in addition to the loot you'd get from dungeon crawling. In Skyrim, this looting is more limited to dungeon crawling, and here you have to be careful not to break/disrupt sideline/miscellaneous or even main quests. In Oblivion, you could also kill wantonly regardless of whether you were in the DB or not. The major difference in Oblivion was that doing so had extreme consequences (i.e. suffering the Wrath of Sithis) if you broke the rules. No such severe consequences in Skyrim.
So from the open sandbox aspect, I think Oblivion gave you a LOT more options for open sandbox exploration due to the expansive citiy/town areas when not questing. And don't forget Oblivion gameplay features like betting and fighting in the Arena which can't be beat.
2) The magic system was more complex and superior in Oblivion (in terms of the number of spells you could cast, perks etc). And Morrowind was even far more superior in the magic gameplay. The downside was the race/class character type you were limited to playing. In order to enjoy the best experience that the magic system in Oblivion (and especially Morrowind) provided, you were somewhat limited to playing the Elven races---particularly the Altmer and then Dunmer Elven Mages. Based on racial stats, these race/class mixes seemed to optimize playing a magical character in these games.