In terms of live play
M13 is simply a stompbox modeller and the HD500 has amp sims I think and a built in expression pedal. I own the M13 and it's sooo easy to use live and sounds amazing. If you have good gear/love your amp tone, then get the M13.
i have a hd300... it can be used as a modeller theres more than 16 models now with the update, it can also be used as a stompbox modeller and a looper, etc.... has a shitload of things and you can customise everything from playing through a combo a stack etc. which key your hamony plays in and stuff like that
I like hd500. Haven't played m-13. I like hd 50O. Variety of effect and amp tones are nice. I got a devil and the hd500 let's me get good metal tones with the effects.