What's faster... an HD CRT or an LED TV

I'm trying to decide whether or not to buy a new monitor or stick with my HD CRT TV.

I'd like to know (sorry if this sounds real nit picky)
how a PS4 connected to an HD CRT TV via HDMI to DVI cable that has to convert a digital signal to 1080i
compares to a computer monitor that has 10ms of lag as seen here


I play the ps3 on my CRT(via component cables) with 0 lag and would like to transfer that experience over to the PS4,
or something as close as possible to it.


Thanks