As far as we understand, the OAT and Grand Circle trips do not visit the same section of the Great Wall. The OAT trip visists a less visited section as compared to Grand Circle. When we took the Grand Circle trip this past October, we visited a most crowded section of the Great Wall, but found adequate opportunity to see the Wall, scenery and get some good pictures, as well as partake in the numerous souveneir shops and restaurants( Grand Circle provided lunch at one ), as well as make purchases from the local street vendors who were selling pretty much the same merchandise as the shops at about 1/3 the price.
If you don't like crowds and want an opportunity to do a bit more exploring on your own, the OAT trip visiting the Wall may be just what you want. Otherwise, the Grand Circle experience will be adequate for you.