Weed isn't as bad as tobacco, but it's certainly still not good for your lungs, especially if you have asthma.
Puff for puff, marijuana smoke is probably more damaging - this isn't scientific, but just compare the harshness of the two, it's clear that weed hurts a heck of a lot more. But if you compare a heavy pot smoker to a heavy cigarette smoker, the pothead might only smoke 2 or 3 joints a day and probably not every day; the heavy cigarette smoker will smoke a pack a day (20 cigarettes) at least.
Also, there are ways to use weed without smoking, such as cooking and eating or vapourizing, which greatly reduces the health risk. An asthmatic person can safely eat as much weed cookies as he/she pleases.
So in conclusion, I'd say weed is much healthier.