I use both, when I need someone to work with me on my system I use teamviewer.  When I need to work with the system by myself it is logmein all the way.  Basically I can set up a constant to allow folks to work on a webserver or other IT things without having to open up my whole system where as with logmein I can pop in and out of all my loaded systems and do what I have to do.

Love them both but I like logmein best.