In terms of lifestyle and quality of life, you could perhaps not pick two more different cities. What they have most in common, perhaps, is that hustle-n-bustle you want to live away from.
This is also, of course, an outrageous question which is impossible to answer but which is fun to take a shot at. With that in mind, I will mention a few things.
For me, the only way to TRULY get away from the hustle-n-bustle in New York when I lived there was to get lost in Central Park or leave. There may be a few other options -- perhaps living in the quieter parts of Greenwich Village....or near Battery Park...but genuine, natural refuges are few and far between.
In LA, there is the whole coast and the ocean to escape to....although depending where you live it can be quite a drive to get there. There are also "rural" feeling communities like Topanga Canyon, where you would never know that you are 20 minutes from LA.
New York is also a classic walking city -- very few people keep cars. In Los Angeles, some people used to not have cars, but they are all dead now.
I hope your plans include at least a week's stay in each city before deciding. Otherwise, I think you are crazy. :-)