I just wanted to throw in my .02 as well, from a slightly different prospective. I'm coming at this as an undergrad at a civilian college, right now in the process of applying to BDCP. Way back in the day, I got my nomination and acceptance to Canoe U, but because of an obligation to my family (had a relative who was very ill, couldn't get by on their own) and in part, this debate, chose to be where I am now.
With a few years of hindsight perspective on it, when I ask myself now if I made the right decision, the answer is that I don't know and never will. I've paid for every cent of my education, in large part because I'm enlisted in the Air Nat'l Guard (feel free to commence with the zoomie jokes) so I've gotten to work with some very good and some very bad officers from all the services and all the commissioning sources. Like several previous posters have pointed out, you can't tell just by watching who came from where unless they're wearing their ring. There are good and bad officers, period; if you have what it takes to be one of the good ones, you will no matter how you get the bars.
That being said their is something special about the service academies; there is a pride and a bond that gets forged their that you can hear in the grads, and that I won't ever fully understand. Is that trade-off worth the real-world experiences I've had? Impossible to tell, but I know that paying for school, living and providing for yourself, deployments, all of the experiences (other than frat parties) that you can get outside an academy that you can't get there are surely going to make me a better officer someday as well.
Bottom line, I'm just repeating what the others have said: it won't make or break you as an officer, but if you feel like it's something you need to do, then you don't need us to encourage you. Good luck whatever path you choose!