At yahoo games the focus is (or was, anyway) on real-time play. You play games serially. You spend a lot of time waiting for your opponent to move. Or, if you spend too much time thinking you take verbal punishment from someone who's impatient.
At Vying Games you can play real-time. But, most people play turn-based (more like correspondence chess). You tend to have multiple games going at once. When you have a few minutes throughout the day you go through your games and make your moves. You don't really spend time waiting for your opponent. You don't feel rushed. This is great for busy people who want to enjoy games a few minutes at a time.
Philosophically, I don't want to get as obnoxious about advertising. I'd rather the site have a more adult (mature?) community. And, I'd rather focus on more obscure (but great!) games where possible.