To the OP:
If you are really wondering which program will prepare you better for private practice, then it is going to vary from specific program to program.
GPRs are typically hospital-based programs, where residents rotate through anesth., trauma, and other programs in order to learn how to treat hospital dentistry as well as the role that dentistry plays in a hospital setting.
AEGDs are typically based at dental schools and NOT hospital based. They are moreso an extension of dental school with residents working in the clinics and seeing a wide variety of cases that other students can't handle.
Of course, there are exceptions to the above, but what I've posted is typical.
Now, having said that, not every GPR will be better than a AEGD, or vice versa. There are some crappy GPRs out there and some crappy AEGD programs as well.
You need to look at specific programs to determine which will prepare you better to fulfill your career aspirations. Don't limit yourself to one type of program. For example, it is not unfathomable that certain AEGDs will provide their students with better casework than GPRs. Sure, there are some cool GPRs at fabulous hospitals in New York and LA and Boston, but there are also some GPRs in rural settings that aren't going to have the patient flow as big cities. The same goes for AEGDs. Go to the adea.org website and find use the post-doc program link to find programs that you might be interested in.
Good luck.