Windows OS
Pros- Very similar to PC version, hence very less learning curve for most people, Good compatibility with PC, large amount of available software.
Cons- frequent crashes, app close key does not close apps, only minimises them, closing process is more cumbersome than necessary, older versions had volatile memory (i.e. memory gets deleted when battery dies), higher hardware requirements, no. of apps not as large as Symbian, runs a bit slow, cheapest Windows mobile handset is also quiet expensive.
Symbian
Pros- More stable, higher no. written apps, interface similar to regular cell phones, lower hardware requirements, very user friendly, Symbian phones don't cost a bomb, can be had even in inexpensive handsets like 6600 with all the functionality intact, large range of models having Symbian, so more choice and higher chances of finding one suiting ones needs.
Cons- latest version has few stability issues, solved only after updating firmware
There are more points i missed out, but these are the main ones. I myself would prefer Symbian anytime, especially Nokia Series 60.