Here's the differences:
-Only one capacity option (4GB)
-Text on each clickwheel was grey
-4GB and 6GB capacities
-More saturated colors
-Text on clickwheels matched the color of the iPod
-Back casing now reflected capacity
Additionally, the clickwheels had different sized connectors, making it impossible to use a first generation wheel with a second generation Mini or vice versa.
As far as I understand, the batteries should be the same between generations.