The obvious difference is the clock speed. The Core i3 380m is clocked at 2.53GHz. The Core i3 2310m is clocked at 2.1GHz and is based on the newer Sandy Bridge core; clock for clock it is about 10% faster than the previous generation Core i3. Therefore, the Core i3 2310m is equivalent to a Core i3 380m clocked at 2.31GHz. Technically, it will be a minor decrease in performance.
The real difference is the graphics core. The Core i3 380m relies on an graphics core/card that must be integrated into the motherboard. In a budget laptop that would mean you will get an Intel GMA 4500MHD. It is not really meant for games, but people have used it to play games at low settings with somewhat decent performance I suppose. For better gaming...