Brand in this case means that YC:
A) Attracts the best startups. If you're going to gun for one of these, YC is at the top of your list. B) Attracts the best investors. It's in the Valley and historically has actually made some investors a pile of money already. C) Attracts acquisitions.
Past performance doesn't not guarantee future returns, however. It'll be a slow change in brand perception, much like an elite school slowly falling out of favor in favor of a newer school.
Not only that, but these companies are becoming regionally specific, which means you'll go to the one in your city first before you apply somewhere else, or that's what I would do anyways.
pg has an active role in the local universities (which are world class btw), and is more philanthropical in his approach with nurturing talent and intelligence. lots of people admire him because of he's genuine. and imo, a lot of these other incubators popping up have alternative intentions. i'm not saying that it's wrong for there to be capital motives, but I think pg's approach is what separates him from a lot of the others.
my suggestion is if you're considering any of these programs, then study their boards, compare the application process, and pick the one that fits you best.
I'm certainly guessing here, but it seems pretty common sense. Ask 100 embryonic startups who are considering this path which investment entity would be their first choice and what do you think you'd learn? I think you'd learn that (if they'd done their homework) they'd pick the one with the longest track record, the best PR, the biggest demo day, the most competitive program (as measured by application-to-acceptance) and the most founders who got rich. YC wins on all of those fronts.
Even if your regional theory holds (it probably does for a meaningful percentage of startup, but plenty are willing to relocate), wouldn't you assume that the bay area has WAY more qualifying software startups who'd be interest in such things and thus (mathematically) would attract more good ones?