I say Croatia first, because of a BIG Greece factor (I gather you have not done any research yet) -- August 15 is a HUGE Holiday for Greeks -- next to Easter, biggest holiday of year (imagine 4th of July & Memorial day & Labor Day rolled into one). Most Greeks leave the big cities & head for islands much of the week before Aug 15, AND after -- so ferries, planes, hotels beaches are not only packed with foreigners but Greeks as well.
Most Europe & UK crowds are July-Aug Because that's when they get their 3-4 weeks off (don't we hate them for that!). It's school vacation too, so retirees, singles & families all jam into jumbo jets & dump on handiest Greek Isles. Aug 20 it eases off a little because school starts. Thus, if you do greece Sept 1-15 you'll have better chance of some beach space and hotel accoms... daytime temps also will be less burny-hot. The sea will be sublime. As for Croatia, August is prime tourist time too, but it hasn't become such a Mecca yet -- and being more northern, will benefit from August temps.