Media Gallery is a native Geeklog plugin where Gallery v1.5.1 is a stand alone gallery system that can be integrated with Geeklog.
Media Gallery has many of the features of Gallery, in fact, I borrowed many ideas and even some code from the Gallery project. Gallery is much more feature rich and is supported by a much larger group. But, Media Gallery has a pretty good set of features and it is a plug and play solution for Geeklog.
It really boils down to what you need in a gallery program? If you want an easy installation into Geeklog, with tight integration with the Geeklog comment system, statistics and security model and a reasonable amount of advanced features, Media Gallery is a pretty good fit.
If you need some really advanced features that Gallery offers, don't mind tinkering with the installation (I've never actually done it, but lots of other have and it seems to work OK), Gallery may be a better choice.
Take a look at the Gallery website
here[*1] and then at the Media Gallery webiste
here[*2] . Compare the features and pick the one that best meets your needs.
Thanks!
Mark