The cable does make a difference. Much of it depends on the cable length.
The longer the cable, the higher the capacitance. The worst the signal degradation.
Essentially, if you are running shorter than 25ft. You'll be fine.
But longer than that, quality of the cable comes into play. When the cable is so long that it stops working, you'll need a HDMI extender.
It's a high impedance buffer that eliminate the capacitance.
Something like Octava HDMI/DVI Extender