Well, I grew up in Brooklyn, but I now live in Queens. I have also lived in Manhattan and Staten Island. My opinion is this...it's not all about baseball (besides, I am a Yankees fan myself...LOL).
There are positives and negative to both boroughs, yet they are quite similar. It all depends on what you are looking for. The second poster is correct, Queens is significantly less expensive to live in that Brooklyn. However Brooklyn's neighborhoods can be a bit more upscale. You have Brooklyn Heights, Park Slope, Windsor Terrace, Carroll Gardens, Dyker Heights, all would be considered higher end areas. While in Queens you have Forest Hills, Douglaston, and others that are nicer neighborhoods.
The commute from Brooklyn to Manhattan to me seems easier, if you work in the city, that can be a deal breaker. There are parts of Queens (closer to Suffolk County) that the city trains don't go near so you are stuck taking the bus.
Yet, Queens that the number one school district in the city - District 26 - which consists of Bayside, Glen Oaks, Floral Park, etc. Those areas are quite nice.
Queens does have a better mall than Brooklyn - I wouldn't step foot in Kings Plaza but Queens Plaza was just recently renovated and well, is huge.
Parking in Queens is arder than Brooklyn. Yet Brooklyn doesn't have the amount of ethnic restaurants that Queens has. And while Brooklyn has Prosepct Park, which is beautiful (so is the surrounding neighborhood), Queens has Flushing meadows park which has more activities. Oh, and yes, Queens does have a beach. Two, actually.
I hope this helps.