What kind of bladesmith are you? If you are stock removal, then useing annealed flat stock and cutting out the blades before profiling, drilling, and grinding, a band saw if the only way to go. It has a thin kerf, can cut in a radius, less noise and dust, can be used for splitting handle material and cutting it out. Also cuts pins, bolster material, Kydex, plastics, bone (no dust, maybe a little), and about anything else you might want to cut.
If you forge, then I would say a chop saw. Most of the steel isn't annealed, its hot (making damascus), it will cut anything, and it is quick. You don't have to worry about knocking 13 teeth off in a row and ruining a brand new band saw blade that cost $11.00 because , oops, it happens. I have both and it is a tremendous time saver. The band saw is a porta band that I made a stand for and the chop saw, I bought at the lumber yard (14"). If you have a torch, you can get by longer without the chop saw to cut, but it isn't faster except in some applications. I haven't tried it yet, but a compound miter saw with a cut off blade (if they make them) would be the ticket. I also had the band saw for a long time before I got the chop saw.
These are a few of the benefits of both and maybe some drawbacks. I hope this helps.