I call shens. Relevant TF2wiki pages:
http://tf2wiki.net/wiki/Minigunhttp://tf2wiki.net/wiki/BlutsaugerThe Blutsauger fires 10 needles per second. If they all hit that's a gain of 30/second, that we can subtract from the Heavy's damage, but it seems very small honestly.
Heavy at point blank does 500-540 damage per second, medic does 100-150. That's too obvious. Let's back up to midrange where the heavy won't hit with all bullets.
Heavy: 50-300/sec, which puts the average at oh...175/sec. Medic at long range: 50-100/sec, or 75. Once you apply the vampirism, heavy is doing 145/sec and medic is doing 75/sec. Heavy has 300 health, medic has 150 health.
So the heavy is doing very nearly twice the damage after healing is factored in, AND he has twice the hit points, all this at a range defined as "Medium range is defined as the main resupply door to the opposite wall on the upper level of 2fort." AND the heavy can crit for what is essentially an instant kill, while the medic can't with the blutsauger. Oh yeah and the medic has to reload in a prolonged firefight.
At long range, battlement to battlement of 2fort, heavy does 50-100 or 75/sec, modified to 45/sec, while the medic does 50-60 or 55/sec. So the medic has a little advantage! Except there's still reloading, and oh yeah, the syringe gun and presumably also the blutsauger don't always fire straight! Plus the heavy still has 2x the hit points.
I'd be interested in verifying your results sometimes, but the math doesn't seem to stand up. Even with the 1-second spin-up time, I would still expect the heavy to win against a Blutsauger wielding medic at ALL ranges. I don't know how you got those results but they're so out-of-line I have to think SOMEthing went wrong.