New mouse is a different algorithm than the normal one, and even allows scripters to modify certain characteristics such as mouse speed and a bunch of others, hardware mouse takes control of your computer’s mouse (and doesn’t let you use it), works best with virtual machines. The default mouse is alright, and has some variations (but speed can’t be modified) so definitely don’t feel obliged to select any options
I personally use new mouse because I feel it’s safer than the normal one
Many people have claimed that hardware mouse is a lot better and safer @Gunmanin particular