You may be aware that there is also a GRASS GIS version 7. So which version should you go for? Well, it depends. Is long-term support, backward-compatibility with the GRASS 6 line and stability important to you. Or do you use the QGIS GRASS GIS toolbox a lot (which is not yet compatible with GRASS 7)? Go for the new GRASS 6.4 series.
Are you always looking for the latest of the latests, or is speed or the ability to handle very large data sets important to you? Have a look at list of new and improved features in GRASS 7. It is still in beta, so in theory less stable. But I should add that I am using this version for some time now (on Linux) and in my experience it is very stable.
Of course, you can also install both, they should run happily next to each other.