When I use the mouse pad, my mouse becomes heavy and slow. It didn't matter whether mouse pad I used, Logitech, Hyperx, or Zowie, it always made moving and latency difficult.
It works well on my table, however the only issue is that it is slick.
I have been using logitech vertical mouse for some time and I have never encountered the issues mentioned by the OP. However, with my previous mouse (wired mouse) I frequently experienced lagging.