Q; Why didn't Picard blow up the Stargazer when he abandoned it?
A; We might assume that Picard didn't set the autodestruct on the Stargazer because it was full of old stuff that everyone knew about anyway. The Enterprise, which is the flagship, is a different proposition, not least for political considerations.
Interestingly enough, when the three Ferengi beam aboard, the Bridge crew who work at the rear station all turn and watch them. This is very, very unusual behaviour for this bunch, as time will show.
Why would they choose to tow the Stargazer when we know it was perfectly capable of flying under impulse power? What would be the point?