What is the difference between influenza A and B viruses that causes their distinct seasonal patterns?
Regrettably, I don't believe we know - we don't actually know why influenza is a seasonal disease in the first place. There are a number of possible theories, discussed in this review, but none of them are compelling enough to be a definitive causal explanation

In terms of the difference between Influenza A and B, B mutates at a much lower rate, which may explain the slower rate of dramatic antigenic shifts, but that isn't enough to disrupt the seasonal cycle by a few months at most.