Why I prefer Oblivion:
-Graphics:
Graphics in Oblivion is obviously much better. Nice grassy landscapes, good looking textures, good animations, especially facial ones when talking to other people. And for that quality is quite optimized, it works quite fine even unless you have too old computer.
-Combat:
Morrowind combat is quite straightforward, you slash, slash, often miss (at lower levels), which is very annoying and blocking is automatic. In Oblivion you must catch the correct timing when to attack or block. Also firing with bow is more realistic.
-Map (the paper map)
In Oblivion you have the main cities already explored and when you discover a location, it is automatically written on the map, which makes you more easily to find those locations where you are given a quest to find them. In Morrowind it was quite depressing searching for those tombs, which you could even have discovered, but then it was a pain to find them again. Also in Morrowind your character had too small view range in local map, so you had to bump in the tomb to discover it.
-Voice acting:
Although they seem that they lacked voice actors, so too many NPCs have the same voice, is quite refreshing to make conversations much more lively and not so depressing as it was in Morrowind, where they only greeted you.
-AI:
I see hardly in any games, the overall NPC AI is very well made, they don't just stand in one place for the whole game, but they wander around, go to inns, talk with other NPCs (where you can hear rumors about various things which lets you make more quests) and go to sleep in the night, usually locking theirselves in their house.
Why I prefer Morrowind:
-More equipment:
This is where Oblivion disappointed me much. It lacks many essential weapons like spears and crossbows and throwing darts (ranged weapons which allows you to use a shield when using them). Staves can be used only to cast spells, you can't use them as a club, so after discharging them they have no use until recharged. Also Morrowind had much more different armor sets, which also could be worn over the clothes, which allowed you to wear more enchanted (possibly constant effect).
-Varied landscape:
In Morrowind you had those mushroom trees at one side, pine trees to other, ashlands, islands, seas, plains, also snow and more temperate climate in Bloodmoon, while in Cyrodill is mostly trees and grass and snow in the north. Also the invisible wall is annoying.
-Fliers:
There are no stuff that fly in Oblivion. So consecutively they cut also you from levitate spell, which was very useful overall in the campaign to create shortcuts and reach otherwise difficult or impossible places. This also renders modding flying stuff much harder.
-Some interface things:
Morrowind has with the yellow bar much more intuitive representation of enemy's current health, so you know quickly what is best to do. Oblivion has that odd semi circle, which at the beginning won't shrink and also at the end it remains that the most shrinking phase more time, so you don't have an idea how much health has the enemy left. Also Morrowind's character status shows all important things at once, you don't have to scroll through pages to find what you want.
-Skill selections:
Maybe is too much, but I still like it, having many skills for different weapon types. Too bad that ranged has only one skill, which is an advantage for ranged specialized characters. Also you had more skills avalaible which let you advance level
-Dwemer ruins:
I just love these.
Maybe I forgot something, but I'll write it down if I notice anything.
To summarize, Morrowind vs Oblivion is quantity vs quality, but in this case I don't think that quality wins, since there must be some essential stuff. It looks that Morrowind is more RPGish, you don't have to rely that much on your skills than your character's unlike Oblivion.
I'm not really a RPGer, but I like games which has little more stuff and decent engine, so I vote for Morrowind.