One is Android and one is Symbian. Totally completely different platforms. Both are however, old and outdated. People know talks about Android 2.3 Gingerbread and Symbian^3 with it's updates like Anna and Belle.
They work quite differently to each other. The experience on both aren't even alike. They don't run the same apps (unless the apps are on multiple platforms). They have a different type of home screen. The notification system works very differently. Different features and different functions. The system works very differently. Symbian now is only used by Nokia while Android is used by a large number of different phone manufacturers.
Android belongs to Google and Symbian belongs to Nokia. But, I reckon Symbian isn't really that good at the moment. I prefer Meego which looks very impressive after what I saw today with the coming soon N9.