You should do both. Tracking thru g ads is more accurate with quicker access to data. Tracking with ga is invaluable for audience building and assessments along with a number of other advantages. You can choose to not "include in conversions" if you're concerned with duplicates in g ads. You'll find both data sets valuable I'm sure. You'll also find them to be different, even if you're tracking the same events and that is interesting, isn't it?