As a counterpoint to Luisa's post, I will tell you that Turkey's Magical Hideaways is our favorite of the many Grand Circle/OAT trips we have taken. We loved the itinerary, even though it didn't include Ankara. We felt it spent just the right amount of time in interesting Capadoccia, and everywhere else except Istanbul. My photographer husband loved all the opportunities he had to capture the scenery everywhere.
As Luisa points out, you have to make this decision based on both the itineraries and on your own activity level. There is a lot of walking, and a lot of hiking, on the Turkey's Magical Hideaways tour. (Some of the hiking is optional, however.) You do need hiking boots, preferably with Vibram soles for the slippery hillsides. We enjoyed the several swimming opportunities in the sea, as well. A certain level of agility is required to climb the ship's ladders and to get in and out of the smaller boats used for ferrying.
One big difference between the two trips is the number of travelers. We love the smaller size of the OAT groups, and always come home with a dozen new friends. ( On the other hand, my mother, who has been on dozens of Grand Circle trips over decades, points out that if you go on Grand Circle, with its larger number of travelers, there are bound to be lots of people you like, while on the OAT trip, you could be stuck with only a few people whom you might not like. This has never, ever happened to us, but..........you never know!) The wait times for restrooms, food service, etc. are always less with OAT. On the other hand, it is a very active, fast paced itinerary, and some people might prefer a somewhat slower pace.
The museums, ruins, natural attractions, home visit, etc. were all wonderful in Turkey, as was the food. Our guide, Yesim, was absolutely outstanding in every way.....She is the best OAT guide we have ever had. And our time on the gulet along the Turquoise Coast was beautiful and refreshing. The cabins were small but adequate, and the whole experience on the gulet was delightful.
If you take the Turkey's Magical Hideaways trip, I think it is important to take the three days in Istanbul at the end. There is so much to see in this large, beautiful, cosmopolitan city, and we are both so glad that we had extra time there for the archaeological museum, Chora Church, some lovely mosques, strolling in the markets, etc. Whichever trip you end up with, you will have a wonderful time!