So I've been to Brooklyn only as many times as I've been to LA. Yet, I'm comfortable passing judgment on LA (Verdict: I hated it until visit #9. Now it's like the cousin whom you appreciate for who he is.), so I guess I'm comfortable opining on Brooklyn.
In a nutshell, Brooklyn is to Manhattan as San Jose is to San Francisco. That is, if San Jose were cool.

San Jose – the more populous of the two cities by 100,000 – is as bitter as a rural Pennsylvania voter, forced as it is to linger in the shadow of San Francisco. Yet, there's a reason that San Francisco came out on top of this sibling rivalry. For all San Jose's economic might, San Francisco has that certain je ne sais quoi that San Jose is most definitely lacking. San Francisco is a global city, brimming with culture and sustaining its own distinct lifestyle. It is a beautiful city populated with strange and fascinating people. The greater San Jose region? Well, it is home to low-slung offices and worker bees. (Even if those worker bees are multimillionaires and are reinventing the world economy as we know it.)

Although the epicenter of New York City's economy is undeniably Manhattan, Brooklyn's status as the most populous borough means it supplies the people required to keep the city going. According to the last census, Manhattan's population was 1,620,867, while Brooklyn's figure was 2,465,326. The only other borough with a population comparable to Brooklyn is Queens, with a population of 2,229,379.
Despite Brooklyn's second-city similarities with San Jose, this is where the comparison breaks down. San Jose, I love ya. But Brooklyn in cool in two ways that, well, you're not.

Second, San Francisco yuppies don't grow up and move to San Jose. Conversely, Manhattan yuppies do grow up and move to Brooklyn. Sure, this migration of thirty-somethings to Brooklyn occasionally draws the ire of committed Manhattanites, but the lady doth protesteth too much. Are these frustrated urbanites afraid of losing their youth by proxy when they see their friends head to the outer boroughs?
Steph & I felt the pull of Brooklyn strongly during a trip to a friend's Park Slope home for brunch a few weeks ago. On the way back from brunch, we walked down 5th Avenue to return to the subway. As we progressed toward Bergen Street, we both got the feeling that – were we to stay in New York – this is where we'd be headed. Turning 30, having a child, and staying on Manhattan means that someday, if you work hard and are lucky, you might have an apartment where TWO (yes, TWO!) people could shower at the same time IN DIFFERENT BATHROOMS. Alternatively, moving to Brooklyn means staying connected to the heart of the city while living in a community that permits you a little more space. To me, the choice would be easy.

What's this? After living in New York City for three years, I'm returning to California. These are the parts of my New York experience that I'll miss the most.