Assuming the same type of shutter, i.e., focal plane. Metal shutters have some advantages and cloth have some advantages. Metal won't burn through if the lens is left pointed at the sun at infinity in a rangefinder camera, or in an SLR with the mirror locked up. Titanium has long been regarded as more durable, that is, can go more cycles, though I don't know why that is the case, if so. It could simply be that the titanium shutter is a part of the more durable mechanisms in pro level cameras. Metal is necessary to form the blades in vertical shutters, as they work differently from horizontal shutters.
Cloth has a couple of advantages. If you accidentally poke a metal shutter while changing film, damage is very likely; less so with a cloth shutter. If the cloth shutter is harmed, repair is likely simpler, consisting of putting parts "back on track", where with metal it means replacement. Getting new replacement metal curtains or blades for older shutters may be impossible, so scrounging used shutters becomes the method of repair. New cloth is easy to acquire.
Finally, I find that cloth shutters tend to be significantly quieter than metal horizontal shutters, and somewhat quieter than vertical shutters, and when the cloth shutter opens, there is usually very little vibration, useful at slower speeds on a tripod.