You always have waits, the question is what wait types dominates your waits.
I assume that you have read up on those two wait types and understand what they mean, so I won't go into that here.
One possible reason is that you don't have the same execution plans for some queries, meaning that the load isn't the same.
Another is of course that the disk subsystem don't have the same performance characteristics. For instance WRITELOG suggests that this is slower for writes compared to the the disk subsystem where you don't see these.