They are both completely different devices, but both completely capable devices.
The Galaxy Nexus is the second newest Nexus device, behind the LG Nexus 4, the current flagship.
It contains a 1.2 GHz Dual Core CPU, 1 GB of RAM, and Android 4.2.2.
Galaxy S3, the previous Galaxy flagship contains:
1.5 GHz Dual Core CPU, 2GB of RAM, and Android 4.1.1, with a 4.2.2 update supposedly coming soon.
Both have decent specs, and either should be fine for moderate usage. Just depends on what you really want.