I used both but this was within CAD (specifically PTC Creo). PTC Creo is menu based with minimal shortcuts, so the screen and extra buttons were great because you didn’t have to go to the menu bar to access the tools you needed.
Within Creo the space mouse was context aware so having the screen helped with remembering what tools you had mapped to the buttons. The best comparison i can think of is hoping between object, edit, sculpt and pose mode and having the spacemouse know this and change the hot keys based on this.
On the enterprise version (don’t think it was on the pro version) there was also an option to store the most recent tool used. It stored i think about 3 of them and would remove the oldest one when a new tool was added.
I don’t know how well the space mouse work within blender and if the stuff i’ve written above would apply in Blender.
Regarding wireless, that is only useful if you want to keep your space mouse at awkward angles, for example having your space mouse between your keyboard and your chest, or you want a clean set up.