I answered this question on the OAT discussion board and will try to remember what I wrote.
I think the most important thing to know is that when traveling solo with OAT or GCT is that you won't be traveling alone. There likely will be other solo travelers and, of course, couples and women traveling together.
You'll get to know others within a couple of days and will find like-minded, well-traveled people. Keep an open mind and learn from their experiences -- both from the singles and the couples. I've kept in touch with both after some of my trips.
I like the opportunity for free time with OAT and GCT so that I can visit museums or wander through towns. I don't like tours that have every minute scheduled -- OAT and GCT's itineraries with optional tours suit me.
I enjoy striking out on my own when traveling but know that I can count on the program directors for information and directions that I need when I want to visit a site that isn't on the itinerary. Since I often get a bit lost, it's an opportunity to ask directions using the local language or a form of sign language. If you are the type to do this, be sure to get a card from the hotel desk to show when asking directions or use to take a taxi back to the hotel.
In Sidney I chatted with a woman on a bus and she told me how to ring the bell and when my stop was coming up. In Buenos Aires, I left the hotel without my map so went into another hotel and the desk clerk gave me a map and marked my route back. In Santiago, I turned onto the wrong street and asked a man where my street was. He put up two fingers and pointed north -- two streets over.
I also like to relax in a park or on a bench along a waterfront and observe people or write in my journal. In Izmir I sat with two Turkish women; one asked in Turkish where I was from and when I said "America" she smiled and told the other woman.
So, for solos, it's the best of both worlds -- there will be people from the group if you want company and time to explore a bit on your own if you want.