I played both Fallout 3 and New Vegas on PC and Xbox 360, consistently the former on both platforms had a ton more stability, even during the early days of Fallout 3's release before any DLC came out. I never experienced even half of the same number of hair-pulling moments like in New Vegas. The newest patch for New Vegas doesn't stop certain characters from vanishing from the game, doesn't lessen the infinite loading screens or interior/exterior transition crashes, and I still frequently see my character's shoulders and gun go above my head when I crouch, just to name a few things that I glaringly remember.
Now, I WILL say that New Vegas took a lot of things in good directions; I liked the reputation system and factions, I liked being able to fabricate a variety of ammunition and weapon modifications, I do believe the character and story writing was superior, the greater number of possible outcomes upon finishing the game, and lots of other things. In most aspects such as these, New Vegas was way cooler, but I couldn't really stand to play it again after just my second playthrough due to frequent crashes and other bugs. Fallout 3, I think I comfortably played it four times with different sorts of characters, once on PC and three on Xbox 360, before I had enough, simply due to pretty much exhausting my ability to find and experience new things.
But since you're gonna play on PC, there are options for mods and unofficial patches that might be able to remedy a lot of those problems. And if no fanmade patches do, if you don't mind 'cheating', you could solve some problems like for missing characters with console commands. If you get New Vegas, hopefully somehow you can avoid the problems I had and have a lot more fun with it.
My Xbox LIVE profile, where you can find my Achievements in New Vegas and Fallout 3:
https://account.xbox.com/en-US/Profile?gamerTag=BetrayerOfNihil (My Xbox 360's hard drive broke a couple years ago and I haven't played since then, so don't add me on here)
My Achievements and game time on Steam for New Vegas:
http://steamcommunity.com/id/BetrayerOfNihil/stats/Fallout:NewVegas/?tab=achievementsI had Fallout 3 on a game disc before Steam, so I don't actually have PC stats for that.
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