Which is the better running shoe of the two? (One Asic, One Saucony)?

I've been running in asics for the past 3 years, so I'd recommend them to anyone. But, the shoe you buy definitely depends on anything you might have wrong with your legs and your stride, and a running store would be the best place to find shoes specifically for you. Places like Dick Pond Athletics, Road Runner Sports, Running for Kicks would be good places to start. There are plenty of specialty stores and even websites that could help you find the right shoe.

I started with Asic and have stayed with them from the beginning. The best thing is to find a good store that specializes in running shoes and talk to the salespeople. I buy online now but I originally went to a store and tried many different brands. They actually allowed me to take them outback for a run before purchasing them.