I think there's a number of factors that go into this decision, and a big part of that is how much you did in dental school, and how much confidence you got from that. Back in the day, 60-80's, you couldn't graduate most dental schools without doing 20-40 units of fixed and 100-200 restorations - during this time, the number of people that did GPR/AEGD was very small. Zoom to today, and many schools are putting out graduates that have done less than five crowns, less than 40 direct restorations, 3 RCT's, and never having picked up a surgical handpiece to section a tooth. Because of this, we have a lot more people (often a majority of the class) wanting to do a residency, because they didn't get the experience they needed/wanted, and haven't built up the confidence / experience they want to go out into private practice.
This isn't to say you can't start working right away, like TanMan said, sometimes that on the job experience can really get your butt into gear, especially if you got a lot of experience in dental school. That said, that won't work for everyone. Every graduating dental student / dentist is different, and there's nothing wrong with needing a post-grad year to fill in the blanks that dental school didn't cover - which are often very large, haha.
Lastly, every residency program is different - some are more or less a 5th year of dental school, and you really don't get much out of them, and can be a total waste of a year with the wrong circumstances. You really need to try to do your due diligence when you're researching where to apply and interviewing. Asking the right questions and talking to the current residents is very important and can make the difference between getting you that bigger leap in skills and confidence, or ending up not much better off than you were a year ago.
I actually attended the residency that I'm now the director of - NYU/L Visalia, Family Health Care Network - and I can say that doing this program was the best decision I've made in my career, and it turned me into the much more confident dentist that I am today.
But, bottom line, it's different for everyone. An AEGD was the right decision for me, it might be for you, or it might not be. You need to do some introspection, and find out for yourself what you're looking for. Also, ask your instructors in dental school what they think, and what they did.
Good luck!