Only thing I've ever had happen that was kinda similar was I had to replace a tire once and the tire the shop put on was a slightly differnent one (different tread). The car would pull toward which ever side that tire was on, because of the different style tread. It would only pull during acceleration though. No other time.
It seems to me that it is possible that by replacing your two front tires with a new set of matching tires might fix this pulling problem, IF the alignment is correct. NORMALLY hard pulling is an alignment or even bent/damaged suspension/frame problem, not tires. Hope this helps somehow.