Oh boy another one of these topics. :P
From a gameplay perspective Oblivion is more accessible and far more entertaining as a whole. Morrowind is more rewarding in the endgame and fits more of a traditional WRPG role. Both are excellent, and both suffered numerous technical glitches at release (Morrowind's were worse though). Oblivion just took Morrowind and fixed the glaring issues in the presentation, combat/magic systems, character customization, and added a dosage of player skill to the otherwise random gameworld. Oblivion had a great balance of this skill and the previous title's randomness. The lockpicking minigame is a great example, where it is still randomized but a skilled timer will find themselves reaping more rewards early on.
However, where Oblivion fell short was the poor leveling system which limited the endgame and ultimately ruined any attempts at exploration (which is one of the things I loved about Morrowind, since both gameworlds are massive and immersive). The argument that Oblivion is dumbed down often comes up as well, and is a quite pathetic one. The idea that the player can influence the gameworld is not in essence a dumbing down, but an evolutionary step in the series. Some point to the lack of certain (many of the times useless) skills which could have and should have been merged earlier in the series.
Oblivion in the long run is the game that most people enjoyed more I would believe. The modding community has proven this time and time again. There are ten times the amount of mods for Oblivion as there are for Morrowind (roughly 20,000 known mods so far, both small and large), and many of these mods helped transform Oblivion into my favorite game this generation. Mods fix every issue Oblivion had, and improve every aspect from the combat to the guilds and much, much more. Modern guns, online play, and much more are also usable thanks to mods (despite many of them being in primitive state). To say Morrowind is better after the addition of mods is downright wrong, as there is a mod that adds the entirety of Morrowind to Oblivion. Here's a few interesting screens from my heavily modded (300+) game.
Character showing a more advanced form of character creation over Morrowind. Not edited (the filter is from the pause menu).
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Bravil.
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Deadly Reflex mod. Allows you to decapitate, slice people in half, chop off hands, crush skulls, etc.
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A screen from one of my favorite quest mods Gates to Aesgaard: Episode 2. Each episode is basically an expansion that lasts 4-6 hours.
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Another quest mod shot, from the famous mod Blood & Mud. A long, difficult questline that doesn't hold your hand the whole way through like many of the vanilla quests. This mod expects you to find your way around on your own, and use the clues to figure out what to do next (there's quite a few great quest mods like this).
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Playing guitar. :P
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