As chip posted, you won't need to change out the dish, just replace the LNB ifyou go for the Genie.
Apart from the five tuners, there's another good reason for going with the Genie. The DVRs (and the HD receivers) are now at "end of life" as far as development is concerned, there probably won't be any new features. And they are not manufacturing them any more. All new development is happening on the Genie.
If you go with the Genie, you need to try to get the HR44 not the HR34, the Hr44 is much faster (and smaller). The CSR will NOT be able to do this for you because direcTV considers them equivalent. When the installer calls, ask him if he has an HR44 on the truck