Simple question, but does "climb better" really mean "climb faster"?

I'm 6'3 and just at around 195# (I could prob stand to lose 10-15#) and ride a 40# commuting rig up ~350ft every day after work. I try to keep the pace at least 8mph, even at 10-11% grade.

On my Lemond CDF (approx 1/2 the weight of my commuter+gear), I can do the same climb averaging about 3mph faster for roughly the same HR and perceived physical effort.

By that logic, if I were to lose 20# of my body weight, should I be able to milk another 2mph at the same effort?