I actually registered after two years of visiting this site at least once a week for ZP just so I could post in this thread.
First of all, it almost always boils down to which one you played first, in my case it's Morrowind. The only things Oblivion has are graphics and spell casting. Many people have already posted most of the following reasons, but just to reiterate:
1. Setting. Like Yahtzee says in his review, it looks like Oblivion copied and pasted the same square mile or so over and over; added some mountains here and some snow there, and you've got the world map. Morrowind has swamps and valcanoes and mushroom cities and deserts.
2. Fast travel. Again, taking from ZP here, what's the point of having a huge world if you can just instantly travel everywhere? I know except for cities you have to discover the places before you can fast travel, but it just seems pointless. Also because of fast travel they removed some of the best spells from morrowind (mark, recall, intervention). I know in Morrowind there were silt striders and the Mages Guild offered some instant-travel service, but you have to pay for those.
3. Levitation. I really don't know why they took this out. It's 4 years after Morrowind takes place and everyone has forgotten how to levitate? Maybe someone can explain it to me.
4. Side quests/Skills/Items. I don't know if Morrowind has more side quests or not (it certainly seems like it though), as I have not actually completed Oblivion yet, but Morrowind definitely has more interesting side quests. There are more skills, and more useable items.
5. Arcane University. I just didn't like the fact I had to do half the Mages Guild quests before I could create my own spell or enchant an item.
6. Creatures. I just liked them better in Morrowind. Those damn cliff racers were something to be feared in yer youngin days, but it added to the suspense of the game.
7. Failing. In Morrowind you could fail at casting spells and making potions (I DON'T like how you could just not hit some things with melee attacks, but whatever), it just made it more believable.
8. Alchemy loop. This might be someone of a glitch/cheat, but in anycase it gave a different playing perspective. For those who don't know, if you create a Fortify Intelligence potion and drink it, your alchemy skill goes up. So make another potion (which will turn out better) and drink it. Loop this for as long as you want, and your Intelligence will be through the roof (so will your Alchemy skill). Then make any potion, say fortify strength. Your strength could go up to 100000 and higher (depending on how long you looped). This kinda removes the threat of ever being killed, but there again you could turn yourself into an awesome being all within the rules of the game.
I could probably go on, but this post is already too long.