Forget the weather - find which has the type of holiday you want. Turkey has a very bad press at the moment due to some of its males not respecting female visitors. nuff said. I went to Bulgaria on business not long ago and found it very interesting. Taxis are extremely cheap - about three quid including tip to go from anywhere to anywhere!
I use to work for a holiday company and from memory Bulgaria was the country with least satisfaction in terms of hotel quality and holiday overall. Turkey on the other hand had a devoted following of clients who returned year after year. It's also likely to be a better bet on the weather.
Only been to Turkey so couldn't recommend one above the other. Turkey is beautiful but beware that their holiday season in general runs from May til September, so what might be a bustling resort in those months can turn into a ghost town from October til March.
been to both in late september, turkey was in mid 30s blue skys for the fortnight. bulgaria was hot but did have showers/rain for 5 of the 14 days. but did prefer bulgaria.