I personally haven't used New Balance at all but I have used adidas exclusively for 4 seasons, this this my 5th season and they are very comfortable provide excellent support and in my opinion are the best brand on the market.
The key thing for you is finding what you want from the shoe in the way of comfort. I feel that Adidas shoes give a more solid feel and stable platform which is something I really like as I prefer the locked in feel especially when I'm bowling. I've heard that other brands are little easier on the foot and more like a cushioned feel but I can't speak from experience.