I would like to install gitorious on my Debian squeeze server.
For doing so I have to install some gems like the ruby database driver for My SQL.
The rubygems approach brings you more flexibility, as you can install any package you like and can have multiple versions of them. If most (or all) of your tools are available as debian packages and the versions suit your requirements, you should go that way.
or is it better to look for Debian packages of these extensions?
Using deb packages as the advantage of having to rely on just one package manager and getting (security) updates for free.The downside is less flexibility, as you can have only one mandated version of a gem installed.The package from Lenny at least used to behave a bit differently from upstream to accommodate the Debian changes.I don't know for sure if that is still the case in Squeeze.
That depends heavily on what software you intend to use.Generally, I'd advise you to either install ALL ruby packages from source (i.e using rubygems) or stick to debs.