Skyrim was mt first Elder Scroll game, but I also grabbed Oblivion and Morrowwind on Steam sales. Haven't tried Morrowwind yet, but I've been mucking around in Oblivion enough to give a general impression. Gonna talk vanilla only, not including mods or console commands.
Oblivion's design feels much MUCH more like a "pen-and-paper RPG" design. Your character has stats and skills, and through the tutorial level you choose Primary stats and seven character-defining skills (called Major Skills). So right from the start your character is placed into a defined playstyle. This is a fun thing for me as I like the idea of creating a character and working with it, but if you like the way Skyrim lets you adapt or change your character build as you play you may not like this. An Oblivion character feels more rigid than a Skyrim character. I am on my third attempt re-rolling a character to get the skillsets working right for me.
Unless I am doing something wrong, you also level slower in Oblivion. My first character was level 6 after a week of play before I rerolled her (Casual play, mind you), while Skyrim I made a new character and got her to level 14 in a couple sessions. Oblivion levels you off your seven Major Skills ONLY, unlike Skyrim where everything you do helps you level.
Oblivion's combat system is also really frustrating for me because the game has no passive health regen and very weak base magicka regen. You start with a basic heal spell that gets really weak really fast and you can burn through your potion supplies quickly diving into repeated fights. I spend a lot of time in my dungeon crawls waiting for my magicka to recharge so I can get my health high enough to continue on in the dungeon. Basically, sustaining yourself on dungeon crawls is a problem for me. And I can't tab-out to do other stuff while waiting on my magicka, because pressing tab opens the character menu and pauses the game, INCLUDING the magicka regen. Skyrim, in comparison, is much more forgiving about sustaining yourself through a dungeon crawl.
Skyrim also lets you dual-wield, and Oblivion doesn't. Sore point for me. XD
However, so far in Oblivion, I do like the "traditional epic fantasy" vibe of the game world. And I am not very far in the main story quest line but I already like it better than Skyrim's. Also, Oblivion lets you fast travel between major cities without having to find them first. You still need to hunt down the smaller caves and areas, but it's easier to travel around from the start.
I would say I like Skyrim more RIGHT NOW, but Oblivion is growing on me. If I can just solve the damn dungeon sustain problem.