Should I spend more days in Greece or Turkey?

You can easily spend 10 days in either country. If you can take more days, do it, you won't be sorry.

Look at Turkey and determine how ambitious your plans are. Turkey is pretty spread out, so to add a single sight adds 2-3 days. So if you are just interested in Istanbul and Ephesus, you might consider trimming a day or two, if you want to add Cappadochia, then ten days may actually be tight. If you have more planned, you are probably out of Luck. Greece on the other hand is easy to add sights to on the mainland, but for islands, figure that each island will be a 2-3 day commitment. So Athens and 2 islands can be done in ten days, any extra time could be added to the mainland to see Nafplio, Epidaurus, Mycenae, Olympia, Delphi, or the Meteora.