Skyrim was my first TES game, but I got really into it. Over the last couple months, I've been traveling a lot and my laptop isn't robust enough to handle Skyrim, so I bought a compilation that includes Morrowind and Oblivion with all their DLCs etc. After loading a bunch of mods, particularly a giant high-res texture pack, and reconfiguring the controls to match Skryim, Oblivion does not seem outdated at all. I tried Morrowind as well, but forgive me fans, going backwards like that was just too clunky to really get into.
Pros: I much prefer the attribute-driven system of Oblivion. I'm not sure if I prefer the static skill-rank base or the perk system for gaining more powerful moves and abilities. The mods available for Oblivion are incredible. I can't even imagine what will be out for Skyrim in a couple of years. It's hard to even think of cons for Oblivion, because it's so likely that someone has modded a fix for it.
Cons: There are some things that I prefer in Skyrim and can't find a mod for, little stuff like making a keyboard shortcut for "take all", giving some external indication that a container or plant has already been looted, things like that. Compared to the more-or-less constant encounters in Skyrim, Oblivion world seemed a little underpopulated. There are many mods that fix this, but finding one that fixes it to your liking may take some effort. I dislike the move lag Oblivion has in third person. Leveling seems a bit anticlimactic, especially since you have to rest for it.
I haven't done much in Oblivion but explore and experiment with mods. I haven't progressed the main quest at all. But it's definitely holding up way better than you'd ever expect a six-year-old game to, and no need to buy new hardware to run it!