I am using both programs (but with different systems).

The main difference between GoToMyPC and Logmein-free is that with the former, you can easily transfer files between the host and the client computers. You can only do that with the paid version of Logmein. You can get around that by emailing a file from yourself to yourself, if the file isn't larger than the max allowed by your ISP.

In short, GoToMyPC is a bit more convenient, but with Logmein, the price is right.