Just to be open with my bias--I am a second-year Goldman student and don't have any first-hand experience with the Kennedy School.
While it's true that the Kennedy School definitely has a branding advantage over the Goldman School, GSPP has opened many doors for me personally. I've been able get very substantive experience in DC (I interned on a Congressional committee last summer and fall and will be working at OMB this upcoming summer). In both instances, my coworkers and bosses expressed very high regard for Berkeley (though it was never really clear to me if they meant the university or Goldman itself). It's true that most GSPP'ers stay in California, but I think there is some selection bias at work. A number of my classmates were California residents before school--meaning GSPP was essentially free compared to other policy schools--and the rest of us out-of-staters quickly discover how nice northern California and the Bay Area is once we get here.
But if you put the work in, there is no shortage of opportunities in DC. While, it sometimes felt like I could have spit in any direction in DC and hit a HKS grad, GSPP does have a small, but mighty alumni network. The silver lining of GSPP's small size is that our alumni are very responsive. Every single alumnus I reached out to in DC met with me, introduced me to other important people, offered advice throughout various application processes, and, in general, has been very generous with their time.
Now the following are just anecdotes, so please take them with huge grains of salt, but I have had several friends and coworkers who graduated the Kennedy School tell me that it is possible to sort of elide some of the harder quantitative content at HKS. That's not really an option at GSPP. The core curriculum is going to force you to wrangle with statistics, OLS, and more complicated forms of econometric analysis. But, like I said, those are just second-hand anecdotes, and Goldman is also far from perfect curriculum-wise.
Then there is the issue of cost, which has more than anything else to do with your individual preferences. My HKS friends took out 100K in debt at 6.8%. I am going to be able to come out of Goldman with less than half of that amount. (I've worked every semester to qualify for fee remissions). Is my degree less prestigious? Yeah, it is. But I have a lot of great career options, as well as the luxury of taking a lower paying job that I believe in instead of having to take a more lucrative private-sector job to pay off my debts.
(And if you're real concern is acquiring the "keys to power," apply to law school. You'll save yourself a lot of grief).