Depends on the assembly house. If they have to make special arrangements for the particular package, then it could be significantly more expensive.
These days, many assembly houses are set up to do mostly surface mount, so through-hole stuff could be significantly more expensive. Especially if you’re mixing surface mount and through-hole or have a through hole on both sides. As for SMT packages, the costs will be similar, though they could charge more for parts like QFN and BGA.
Read More: BGA PCB Assembly