Have you actually measured the draw weight, or are you just going by what's marked on the bow?
Are they identical bows, or different model bows that happen to have the same stats? For example, if I had a longbow braced at 7", and a recurve braced at 8 1/2", both center cut (but not cut past center) I would expect the longbow to shoot to the left of the recurve, since when the arrow leaves the string, the arrow fired from the longbow will be angled somewhat more to the left than the arrow fired from the recurve.
If the bows are made out of different material, even if they measure the same weight, it will be found that one bow will be more efficient than the other (deliver more energy to the arrow). This could be noticed by shooting the same bare shaft from each bow, and noticing that the bare shaft from one bow impacts the target at a slightly different angle than the other bow.
For example, I have an older model 65# BW and a newer model 60# BW. The newer model has bamboo in the limbs, and is more efficient than the older model. They both happen to shoot the same bare shaft the same, as close as I can tell. Which is nice, since I can practice with the same arrow with the 65# bow that I hunt with in the 60# bow, and expect the trajectories to be the same. It's sort of the opposite of your problem, but illustrates the point.
I'm sure you wouldn't even notice the difference if it were the only bow you were shooting, since you would just adjust. I had a similar situation with my DAS bow that wanted to shoot to the right of my other bows. Fortunately, I could adjust the arrow rest to eliminate that problem. Otherwise, I don't think I would be happy having bows that wouldn't hit in the same right/left orientation.