It is true that I shouldn't run apt-get and aptitude on the same machine?

See David Pashley's answer here for more information.

Well, aptitude is more modern, and has at least one feature that apt-get lacks: aptitude tracks which packages have been installed due to dependencies (and not by explicit user request) and removes them automatically when the packages that needed them are removed from the system. Edit: Actually, recent versions of apt-get also do this. However, apparently aptitude's conflict resolution is more advanced than apt-get's.

Also note that aptitude is now preferred over apt-get. But apart from the issue noted above both are perfectly compatible and can be used side-by-side.

BTW, note that you can also use aptitude directly from the command line, e.g.

aptitude install foo

So if you only use apt-get for direct installation, you can switch completely to aptitude.