First off, if you aren't competitive for your desired dental specialty by the end of your third year, then the first thing you should do is get as much advice as possible and take steps based on that advice. Don't make decisions on your own. AEGDs and GPRs are typically quite different, and depending on the specialty you're pursuing, one may me preferable to the other (or perhaps neither are good choices).
AEGDs, for all intents and purposes, amount to a fifth year of dental school. You take on some tougher cases and you have much more autonomy. A GPR is an entirely different animal. GPRs are hospital-based residencies designed to expose you to medicine as well as more advanced dentistry. In a GPR, you will certainly learn to handle more difficult dental cases, but you will
alsorotate through various medical specialties like internal medicine, anesthesiology, cardiology, maybe even OBGYN (yes, I've heard of this in GPRs). As a result, you come out more in-tune with the medicine side of dentistry than you would upon completing an AEGD. Am I biased towards GPRs? You bet. I myself didn't do either.
As for entering private practice, you can certainly do so. Keep in mind, though, that you're rarely better off doing that than, say, a GPR or AEGD. To my knowledge, some specialties (endo, for example) like residents who have some private practice under their belt. If you're ultimately interested in OMFS, however, then private practice as a general dentist will
not help.
I am a DS2 who is thinking about specializing. I've heard that that an applicant thinking about applying to residencies can improve their chances by having experience practicing after dental school. So my questions are...
What is the difference between GPR and AEGD? They sound like nearly the same thing.
Do you pay tuition to be in these residencies (GPR or AEGD)?
Why would anyone who wants to supplement their application with a year or 2 of experience choose a GPR/AEGD when they can go into a private practice as an associate and take home 100k and then apply? You get experience either way, so why not get paid?