The HR44 came out in 2013. 13 years ago was 2011 (the same year I got D*), and the current DVR for new customers back then was the HR24.
You should keep the new HR44, in case you had any problems with the old one and also because like you just found out, the Gemini works with it.
HR44 and HR54 are two different receivers,
HR44 came out in 2013, HR54 came out in 2015.
When I got my Genie upgrade in October 2016 though, I was given an HR44, not 54.
A big difference is that the HR54 doesn't have any touch buttons on the front, other than of course the D* logo power button.