Get both. They are both great games. I do agree NV is the glitchier out of the two, but I also feel it has greater storyline depth to it. Not particularly the main story, but just all the little pieces together, and having companions that have their own thing going on, some greater than others of course, was also nice. I think the main thing is that New Vegas feels more like what Fallout should be, whereas 3, while still great, to many did not have that same feel. Keep in mind both 1 and 2 took place in the western US, in the California areas. I completely disagree with Prime in saying NV didn't mesh well with what fallout is supposed to be, but I guess different strokes for different folks.
Honestly since you can get all the DLC together in one nicely priced shebang, I would go for the original Fallout 3. I have actually heard that they plan on doing no less than 9 DLC for New Vegas, though I have no confirmation on it, so it may be best, if your willing to wait, to see how that pans out, and just get the GOTY edition of that once it hits. Also the game of the year for fallout 3 shouldn't be that hard to find.
Also the games do not really interact with each other, so you are not really "missing out" if you play NV before 3. In fact if anything, playing 1 and 2 will have you smile occasionally doing NV due to little things here and there from those games. Well 3 had one moment of that, that I can think of, but NV has more of it in general.
So thats my blah blah on all of this.