I have the 180mm f/2.8 Nikkor, and yeah, it's sharp, but I don't find it any sharper than my 70-200mm VR, in fact, I'd say it might even be less sharp. But, the difference is tiny at most. The biggest difference, beyond zoom, and VR, of the 180mm and 70-200 is the auto-focus. I shoot ice hockey with the 180mm ('cause I just got the 70-200 today) and the focusing is slow, even on the D300, but especially slow on the D80. If you are comfortable manually-focusing the lens for sports (which is what I do for hockey, yeah, it's hard, but doable) then the 180mm may work fine for you. It's $800 or so, right? I mean, I'd consider maybe going with the 300mm f/4 which you can find for $1200 I think.
The 180mm is a pretty short lens, physically. Only about 5" with the lens hood (built-in, nice) not extended, but it's a dense lens. The thing is a tank, it's really durable and because of it, a bit heavy. It doesn't balance well with my D80, but it balances better with my D300 and battery grip. The 80-200 is about the length of the 70-200 (which is pretty damn long) but I believe the 80-200 weighs more (someone correct me if I'm wrong). I'm not sure how effective VR is whilst shooting sports, as I've not used my 70-200 for sports yet. The 80-200 is supposedly a really good lens, so I'd not overlook that at all. And yeah, my experience with the 180 says that it's a good lens for manual-focusing but it might be too short for some sports, dunno. I have threads in the Photojournalism Gallery of UMaine hockey, in which I used the 180mm, and also one of Portland Pirates hockey, so if you want to see some examples, go check those out. Those were taken about 100 feet from the ice, maybe 150, or maybe 80, I'm not sure HAHA. But that'll give you some idea maybe. I hope this helped. And yeah, sorry for my disorganized reply.