AS a women alone I would choose Greece over Turkey, I have been to Greece( specifically the islands of Paros and Mykonos for two weeks) and travelled as a young lady with a friend and other then alot of flirting found it fairly safe. We only spent one day in Athens as we did not find it quite as "safe" feeling, it being a big city and all. The islands are welcoming though. My friend then stayed an extra week alone on Corfu and had a great time.
I have not been to Turkey but another friend went with her husband, and found the attitude towards women a little less pleasant. She was glad to be with her hubby.
Personally I wouldn't actually choose either, I would hightail it to Paris, where I have been alone several times and always felt very safe and even dining alone there is normal.