As mentioned, if there is only one criteria, SUMIF/COUNTIF will beat SUMPRODUCT hands down for speed. These functions are optimised under the sheets to test a criteria over an array, SUMPRODUCT uses the array approach, testing them one at a time.
You can also simualte multiple conditions if they are simple using say COUNTIF. For instance, this SP formula
=SUMPRODUCT(--(A2:A200>=--"2008-01-01"),--(A2:A200<--"2008-02-01"))
can be achieved with
=COUNTIF(A2:A200,">=01/01/2008")-COUNTIF(A2:A200,">=01/02/2008")
and the latter is still quicker