I had to make this decision as well and I am choosing Einstein. Being in NYC is a huge asset, as you will find over the next four years. On top of that, Einstein is cheaper and generally considered a better school, whatever that means.
I love the Bronx--it is not exciting, flashy, or trendy. It is raw New York, as real as it gets, without any tourists or transplants. The borough gets a bad rap because of the crime and poverty plaguing much of its southern portion, but the northern stretches have some fine blue collar to upper middle class neighborhoods with no frills.
The truth is, nobody really goes to the Bronx except people who live there or for Yankees games, so much of what you hear about the borough is not based on experience. It's just a place where New Yorkers live. Again, not an exciting place to live, but not dangerous. At Einstein you'll still be in the shadow of Manhattan, and that is a great opportunity. You will have access to all the benefits of living in New York City and you'll go to Manhattan plenty--it will just take you a bit longer to get there.
Both Philly AND the Bronx will both be a huge culture shock for a west coaster. This is a good thing, in my opinion.
--someone who may or may not live in the borough bordering Manhattan to the north and east