Note: this turned out to be a very long post. For a quick answer, just read the first paragraph.
Definitely Morrowind. I've played both games a lot, but somewhat ironically, haven't actually finished the main storyline of both. Both have their pros and cons, and I can say I enjoy them both quite a lot, but Morrowind has provided me with a richer, deeper experience in nearly every aspect.
It's early morning here and after a sleepless night my mind is clearly not up to its best, but I'll try to bring up the points that influence my opinion:
Morrowind: I'll start with the thing I love the most about it, and that is the setting and lore. It's quite unlike most other fantasy-themed RPGs out there, and although not entirely original in all its aspects, it brings all those different layers and cultures together very well. You've got the rich and long history of the Dunmer, remains of the Dwemer civilization and their artifacts, the presence of the Empire, the political and religious struggle between all the Great Houses, Empire, Temple and, of course, the Tribunal; living gods. The number of factions present, either joinable or not, is much greater than that of Oblivion. However, what I like the most is the huge amount of lore put into the world - it can be seen in the different styles or architecture and equipment, as well as the rather impressive amount of in-game literature available for those who are willing to take their time with exploring the world. Despite lots of things being "behind the scenes"; not fully present in the game, it feels very much connected.
...there are also much more items, weapons and other equipment of all sorts present in Morrowind than Oblivion. Having choice is always a good thing in my book.
I actually prefer the text-based conversations over voiced dialogue for two reasons - firstly, having these walls of text, although somewhat unrealistic and not fully reminescent of conversations you'd have with people in real life, allows the developers to provide player with much more information of all sorts; telling more about the world and stories taking place in it. Secondly, it makes modding and writing your own quests and stories much easier and resource-demanding. Dialogue added by mods doesn't seem to be out of place.
...Of course, combat as well is an important aspect of both games. The simplified combat of Morrowind can really break the immersion at times, but as long as I view it as an abstraction of combat, instead of a simulation or direct representation of it I don't have much problem with that. Ultimately, character skills having more influence over the outcome than my own reflexes result in a more careful planning and tactical thinking. Every encounter means me weighing out the damages received, resources used and potential gains. There are times when it's better to sneak past and avoid fighting, until I find better means to deal with that particular enemy. Lack of magicka regeneration means it's a resource that requires a bit more long-term planning when spent.
Engine limitations, such as wooden animations and lack of proper hit-detection, absent physics and exploits in AI behavior - such as their inability to use doors to travel from one are to another on their own, as well to interact with the environment in any way both break the immersion and greatly reduce the gameplay possibilities. It's a huge disadvantage, especially now when we have technologically much more advanced games, but apart from some minor things, there's nothing that can be done about it.
The world of Morrowind, despite being rich in lore, has always felt very static - which it actually is. Even after hundreds of hours played, the world looks just the same way as it did at the very first glance. Memories of all the things done and experienced, as well as the general sense of immersion compensate for this, but if their effects suddenly (or gradually) leave me, it turns into what seems a shallow, artificial world and experience (despite the AI routes and added detail to the environments, same thing happens to me in Oblivion at times as well. Here I am hoping that the world will be more dynamic and responsive in Oblivion).
Oblivion: I'm noticeably more tired than I was when starting this post, so it might be lacking any new ideas; at least at this moment.
The setting: when compared to that of Morrowind's, Cyrodiall seems way too ordinary and lacking variety. I've really got nothing against the forests (except for the grass that obscures the view way too much) that are seemingly everywhere - they can be fun to traverse and nice to look at; going hunting in them never really seems to get old for me. Yet, something different every now and then could have helped a lot; providing a temporary change and change of pacing. Playing Morrowind is more like writing a personal story of my character - she's still just a model, and avatar without any personality, but all the experiences and changed of pace: spending time in the dangerous Ashlands or peaceful South mean really different experiences to be had - linked together, they make a story. Oblivion is more playing against the rules that make the world; meta-gaming and not writing a story (Gain X levels; collect full sets of items; get the best armor in the game; clear every dungeon in the area; complete the Thieves guild quest line before moving to the Dark Brotherhood etc.) Most things in Oblivion seem to be built around that artificial metagame.
I wish there were more choices to be made in both games, but Morrowind's faction system that meant I couldn't join all the factions and do all the quests out there added to the immersion. Lack of proper feedback when such choices are made, however, is not a thing I like (it's often not possible to know I've made some other quest incompletable, for example.)
Combat itself feels much more satisfying, but the system is still not flexible and dynamic enough. I think Dark Messiah got it right, but such deadliness in combat, in what is an RPG game, might not be what everyone wants. Oh, and I love the combination of bows, stealth and poisons. Magic helps too, but planning those one-shot kills and executing in a swift manner is most satisfying. To me, that is. I'm the kind of person who almost always ends up playing as a stealth character (Note: it can also make game much too easy at times due to exploits in AI and other issues that break the balance.)
What I enjoy the most in Oblivion is actually playing that metagame. Clearing areas, maximizing profit and developing alchemy and magic combos. Just running through forests (and killing everything that moves with a bow). Exploring dungeons and planning each approach and combat encounter.
Morrowind has more nostalgic value to it for me. When I first got the game, it was a Russian localized version, and at that age, I barely understood a word in it. The first few hours were full of frustration both to the language barrier and complete lack of experience with action RPGs before. Still, it was a memorable and just amazing experience to explore a such alien world in a computer game. I decided to make my final playthrough of it last year, but a hardware failure interrupted my plans. I have the installation files with all carefully adjusted settings and mods (about 25-20 of them) saved and I'm sure I'll restore it once I have my PC fully working again.
