*Disclaimer: I am just posting these stats to show an example of student plans after attending Penn (in my case and where these stats come from) and I'd imagine the other Ivy schools. There's no way I'd be able to attend this school without the financial aid of the HPSP, and would have gladly gone to my state school if I did not have it. This is not an argument to go to an Ivy or to not attend a state school.*
2013 grads plans after graduation: 46 specializing (10 OMFS, 12 ortho, 7 pedo, 4 endo, 4 OS internship, 2 perio, 1 perio-pros, 3 pros, 3 military specialty), 36 GPR/AEGD, 52 private practice. Numbers were very similar for 2009-2012 grads as well.
I'm not sure of the numbers for state schools, but I'd imagine Ivies have a higher percentage that specialize (or those that want to specialize going into dschool in the first place). The name, as of now, I would assume plays a part in these results. But, as many others have stated in numerous threads, you can specialize from any school you go to, it just may be easier to depending on the school.