I would agree with most of the posters here that you don't NEED to have watched BTVS to watch Angel but at least the first three seasons of BTVS give some background on Angel and some of the characters who join him in LA (i.e. Cordelia, Wesley).
I enjoyed both shows immensely despite being initially unsure about BTVS (I thought it would be modeled more after the corny movie with Kristy Swanson). After watching the first 4 seasons of BTVS, my wife bought S1 of Angel and we continued collecting the seasons on DVD as they were released. In conclusion, I felt that Angel was, in general, much more solid show in terms of writing and quality of episodes (I particularly enjoyed most of the the non-stop S4 arcs) than post-Season 3 BTVS ended up being (although S5 was rather good). It's too bad that there only ended up being 5 seasons of Angel as opposed to the 7 seasons that BTVS got. OTOH I'm not sure where else they really could've gone with Angel after Season 5 given the conclusion that the writers came up with not to mention the fact that Angel is immortal and that there wouldn't really be a good way to end the show absent his death.