They're all 1:6 scale of course, as you know... I've never seen a BBI 12" figure opened to really compare it much to my Dragon figures... I believe, but don't quote me, that Dragon's a substantially higher quality than BBI, but BBI's higher quality than 21st Century Toys...
I'd say if you were comparing, Dragon and Sideshow are probably more comparable in quality overall.
As far as accessories, I'm assuming you mean do the hands of a BBI figure fit a Dragon figure? I can't be 100% sure but I would think that they would. Again though, I'm just not terribly sure.
Gear like clothes, helmets, etc... That all is universal generally. Dragon gear should fit a Sideshow figure, or BBI, or 21st... I've never run into problems interchanging gear like that. The hands issue though,t hat could pose a problem for ya Chris... Though in general they're similar constructions, at least at the wrists.