Funny, I was just going to come on and do a search for this question as well as I'm considering braids for 6 weeks and then possibly a weave for 8 weeks for the LHCF Bootcamp '08.
I've worn weaves for 2 years straight (not giving my hair a break at that -
yeah I know, I know), but I took good care of the hair underneath and I saw tremendous growth. My hair started off as a short fro, then went past my shoulders and is VERY healthy and thick. I recently got a cut to an even SL and started my journey since wearing my hair out. I always ONLY did sew-in weaves and used quality custom hair which I ordered online. It worked for me.
I'm considering braids now for something new. I'd be a little worried about my edges thinning, I'm considering small/medium sized box braids though to prevent this, and my stylist I'm sure wont dont them so tight that breakage occurs.
For me I loved the versatility of the weave, but if you leave your hair out it's definitely more maintainance because you have to take care of that AND the hair underneath in the tracks, and then there's styling the weave as well (I liked wavy textures because I could do wash and go's and look good, or mist it with leave-in and be fine). Also make sure you match your own texture as close as possible to avoid having to straighten the hair you leave out to blend with the weft hair. Again with wavy styles you can kind of even do a braid out with the hair you leave out to blend, and you can sport a straight look if you roller set and wrap.
I havent worn just braids in so long, so I cant tell you my point of view about that, but I would see it as a little less hassle to maintain, so maybe you can consider switching btw the two...