The problem is: With Mac OS X 10.15 Catalina, you don't have a choice, since eyeTV 3 is not 64-bit ready.
As it is, eyeTV 4 is pretty much unusable, and I would expect MUCH better support, and software, very soon!
BTW: eyetV 4 tends to fail to detect my eyeTV netstream 4C for days on end, anyone else experiencing this issue?