The human eye, at any particular instant, can perceive contrast ratio over a range of 400:1 to 10,000:1 according to numerous references. However, the human eye is a dynamic organ and can adjust, both chemically and via iris movement, over some 30 minutes in steady light conditions to perceive higher contrast ratios of up to between 1,000,000:1and 10,000,000:1. One can think of the eye as an adaptive detector. Age is a factor influencing what contrast ratio might be perceived by the particular individual.
The images displayed can affect the perceived contrast ratio with the human eye being able to detect higher contrast ratios for static images as opposed to moving images.
Ambient Light Conditions
Even small amounts of ambient light (one LUX - a candle flame) significantly reduces the ability of display devices to render higher contrast ratios (in the 1,000's). A black area can only be as black as whatever incident light is reflecting from it. You cannot "project" the color black. Doubly detrimental is the rapid drop off of the eyes contrast sensitivity with higher ambient light levels.
Spatial Frequency
The eye is sensitive to the spatial frequency which is a factor related to the distance between the contrasting image elements in relation to each degree of field of vision at the eye. Consider that the frequency is the count of the number of alternating vertical stripes of black and white across an arc of one degree with the eye as its origin. Increasing the number of vertical stripes across the arc (making them thinner) will, beyond a certain point, reduce the eyes ability to perceive contrast ratio - even though the actual contrast between the white and black stripes remains the same. For a practical demonstration of this concept try this dynamic demonstration of the eyes variation in contrast sensitivity with spatial resolution by the USD Internet Psychology Laboratory.
Differences in contrast ratios in the multi-thousands should only be a consideration in choosing between display devices when you are going to place them in a strictly controlled, very low ambient light environment - something like a windowless home theatre room with dark finishes on all walls and surfaces.
For higher ambient light viewing environments brightness should be a much higher rated selection criteria than contrast ratio.
There is no substitute for judging between the image quality of displays than viewing them side by side with your own eyes in a viewing environment with an ambient light level similar to where they would be located.