From what I've heard in the past, and what I just read in this thread, I wish I had played Morrowind, but I was never a PC gamer, and I don't really have the computer to handle much gaming anyway right now. Unfortunately for me, the console I have is the one TES seems to hate, so my PS3 just frowns at me and apologizes when I have to turn it off and on again when it freezes and when the save data size increases rapidly.
Regardless, of the two I've played, I'm not sure if I could really choose. Oblivion had the Unarmed (or was it Hand to Hand?) skill, one of my favorite characters to make being a hand to hand one. The Dark Brotherhood was much more twisted, which I loved since it's only to be expected that the group of assassins is dark and twisted. I also felt as if the storyline was a little more immersive than Skyrim. Helping out the heir to the throne and saving the world from the Oblivion crisis just felt like I did more than slay a really old dragon that ended up being a complete chump. I also loved going through all the portals, though similar, always different enough to mix things up.
As for Skyrim, like is obvious, the graphics were better, giving me a more crisp experience. Slaying dragons was fun, and all of the shouts gained created even more fun. My roommate creating a Fuhrer Bradley character from FMA was also fun, using the shout that increases attack speed, as well the slow time shout at other times, coupled with the time slow while blocking a power attack made him very fun.
Before digressing too much more about specific characters, I also loved dual-wielding from Skyrim. Whether it was two melee weapons, a weapon and spell, or the traditional shield and sword that Oblivion also had, I felt like I had enough options to keep me interested. The only thing not possible was two shields, but that's just ridiculous :P The perks were also fun, though at times I felt like the number I could, even after maxing out my level, could become too limited with a broader, less specialized character.
Overall (and in no way is that all I have to say about the two games, I just don't wanna ramble and repeat myself somewhere), Oblivion had me with some quirks and storyline, but Skyrim had me with the battles, graphics, and dovahkin-related features.
If I really had to pick one, I think finisher moves would tip Skyrim towards being the winner, but both were excellent games in my opinion, even if I get no DLCs for Skyrim.
*goes and cries*