Most people won't notice much if any difference. 4 ms = 1/250th of a second. At 60fps and 60hz, one frame is about 17ms. If you were getting 250fps in a game on a 250hz monitor, it would be the equivalent of lagging a single frame. Pro gamers who make their living in milliseconds sure, though it's more a matter of feel than precise measurements. And they'd never run a 4k rig anyway since even dual Titans won't push 300fps at that res.
The marketing fluff over contrast is between dynamic and static. Both measure the difference in brightness between the brightest and darkest color the panel can display. However, a monitor can't be at both its brightest and darkest at different points of the screen at the same time. The backlight has to turn all the way up or down to achieve the extremes. Static contrast measures the maximum difference between two pixels that can be displayed at the same time. Dynamic measures the difference between two pixels displayed at different times.
So dynamic ranges stretch all the way into the millions because they can compare say, two pictures taken at different times. Static barely reaches into the thousands but you'll notice it far more. Ie, anytime you're looking at the screen it's displaying its static range. You only see the dynamic range when the image on screen changes, like trying to compare two pictures from a slideshow by flipping back and forth between them, and never seeing them at the same time.
For games, a really crappy contrast ratio makes everything either too dark or too light. That shouldn't be a problem with either of these, or most modern panels for that matter. Graphics pros would care more about color accuracy than contrast. Personally, I went from a a TN panel to PLS (plane-line switching, practically the same as in-plane switching) and haven't looked back.