I understand that you want to know if you can get a better A/V signal if you upgrade to the Slingbox PRO-HD.
As you said, basically it all depends on the connection speed you get on both ends (Slingbox location and remote location). Keep in mind that if you get the Slingbox PRO-HD, you will need a higher connection speed that the one you currently have. It is not necessary for you to update your Direct TV receiver.
The following links will allow you to get some information about the requirements for the Slingbox PRO-HD and some other useful information: