Honestly, if you don't mind dated graphics and turn-based combat, then I don't see why you wouldn't like them. Looking past the limitations that an old engine and turn-based combat mechanics have, the story is really great, characters have some substantial depth and, as far as Fallout 2 is concerned, it's maybe the only game that really allows unlimited freedom to the player; what ultimately restricts you is the consequences of your actions. Oh and sneaking - it doesn't work.
I think they've aged fairly well, all things considered. And with mods in the scene, there's a lot of replayability for both games. I'd suggest looking around for some compatibility patches, as I've had some minor visual issues with Fallout 2 when running it on anything newer than Windows XP. I think that using the compatibility mode and running the .exe as an administrator should fix any issues. I didn't bother checking since, as I said, it wasn't anything even remotely gamebreaking - just some wayward pixels that were the wrong color.
Then again, if you get them through GOG or wherever, things may be different. I was using an original disk when I first played it, which I subsequently copied, so something might have gotten messed up during that process.
Lastly, I'd strongly suggest playing Fallout before Fallout 2. Their stories aren't all that strongly connected together, but Fallout one has a time limit which annoyed me to no end, having Fallout 2 beforehand, where there's no real concern about finishing the main quest on time.