Yeah, any decent blutmedic should beat out a pyro in normal conditions. At least, provided things like they both have full health, the pyro doesn't get the drop on the medic, blah blah blah. Unless the pyro is smart or something, but how often does that happen?
I'm a pretty damn good pyro (read: 12 arrow reflect kills and numerous rocket/sticky reflect kills in 2 hours on 2fort today; able to airblast rocket jump and airblast nade jump), and I honestly couldn't tell you how I'd beat a blutsauger medic.
If he's in flamethrower range in the open, it's pretty much luck that he doesn't dodge around too much. No matter how perfect your aim is, you can't force a flame particle to not miss.
If he's at the edge of flamethrower range, you lose automatically. Not even the shotgun is going to win that fight for you.
If he's in flamethrower range in a cramped area, there's always the chance of puff'n'sting, but if his aim's good there's still a fairly good chance you could die before you get the killing blow.
If he's standing at long range, it's a guarantee he won't kill you, and flares have a slight chance of not being dodged. Realistically, both parties would either retreat, or waste ammo trying to fight long range before getting steamrolled by each others' teammates.