Forget Fallout 3; this is the definitive Fallout experience
Before I start the review, I'd like to point out that I played the game with every piece of DLC installed as found in the Ultimate Edition. As such, my experiences, and thus my opinion of the game, may differ from your own.
Fallout New Vegas, with all due credit to Bethesda, is better than Fallout 3. Obsidian, the developers of the game, took what was great about Fallout 3 and improved it, while getting rid of some parts that just didn't fit. As a result, Fallout New Vegas, more than just an expansion pack, is its own game, and a better one at that.
The story of Fallout games has never been a key feature, and this game is no different. You're a courier who's been shot in the head and left for dead, and without delay, you immediately head off to find who shot you and for what reason. Of course, the great part about any free-roam, open-world game is that you don't have to do the main quest first, and any curious player will immediately find loads of sidequests to do first. The story is pretty unremarkable, though the characters you'll meet along the way are somewhat interesting. Sadly, the game does not allow you to continue your game after completing the final mission of the main quest, so you'll probably want to leave that until you've seen everything the game has to offer.
On that note, the game offers so much content that I feel I've barely scraped the surface in all of 30 hours. Granted, I have the DLC packs installed, so this expands the length a bit more. The great part is, the missions never feel stale. Oftentimes the problem with open-world games that feature many missions is that the missions eventually feel repetitive. However, I never felt that with New Vegas. All of the DLC with the exception of Dead Money is great, so if you are able to pick up the Ultimate Edition, I would recommend doing so.
I won't go over the individual mechanics of the game, as this would take quite a while. However, let me just say that the bugs have been noticeably fixed from release, at least on the PC. In fact, I rarely saw any bugs, the most grievous of such being some wacky physics bugs with ragdolls. So if you've been turned off the game at the prospect of these infamous bugs, know that they've been fixed, and the game is very much playable. A must-buy, in my opinion.