SUMIFS is more efficient overall but SUMPRODUCT is far more versatile.

The big difference between the two is that SUMIFS can only be used for straight comparisons. You can't "manipulate" the criteria while with SUMPRODUCT you can "manipulate" the criteria.

For example, in SUMPRODUCT you can do something like this to manipulate a criteria:

MONTH(A1:A10)=5

You can't do that in SUMIF(S).