You want to keep Vista on the old computer, but also use it to qualify for Upgrade version on the new one?
Under the EULA the XP or Vista qualifying for using Windows 7 Upgrade version cannot be used during the period it is qualifier. So you couldn't use it to qualify if you intent to use it on the old machine, too.
If you want to delete Vista off the old machine and it is full retail version, you can use it to qualify for Windows 7 Upgrade on the new machine. It isn't even necessary to install the qualifiying XP/Vista to use Windows 7 Upgrade version- you just need to have it on hand and not use it while qualifier.
Hope this answers your question.
You can directly install Windows 7 using one of the workarounds given in this tutorial to activate Upgrade version on a clean or wiped HD: Clean Install with a Upgrade Windows 7 Version