Slightly differing colors or brightness may not be a problem. But If something just can't be seen, thats' a problem. Many screens add exessive color saturation or boost the contrast only to be "more impressive" when they're used for movies or games. "Impressived" or simply wrongly adjusted screens destroy details in dark or bright image areas or both. The details will be flattened off.
The wrong adjustments can be done in computer's graphic card, too, if it allows color, brightness and contrast adjustments. Most of them allow.
See the following gradient:
There are white and black irregular zigzag curves over a smooth gradient from black to white. In theory the both zigzags should be visible from left to right except at the ends, where the background and the curve has same brightness for 1/256 of the width. If the invisible part is longer, then the screen is too dark, too bright or tries to boost the contrast.
In practice on "not at all too bad" screen the total length of the invisible parts may be as much as 5...-10 % of the image width. I have noticed this to be accumulated into the black end because the screen is intentionally adjusted to be dark for more covenient average brightness.
The background gradient and zigzags should not seem to be colored anywhere, because it's RGB grey. The gradient has 256 steps. One step is 4 pixels wide. If the steps seem to be wider, then your screen probably has less than 256 brightness levels. It was common about 10 years ago, but today it's rare.
Put the test image onto your both screens and compare. Explore the settings of the screens and videocards to find as even color, brightness and contrast as possible for both systems.
There exists a concept "Gamma" and you probably find its contol, too. It's used to make the apparent shift from dark at left to bright at right to be as uniform as possible. The apparent mid grey is in the middle if gamma is ok.
To be exact, this test should be done also by using 3 similar images, in which the white is replaced by R, G and B. It reveals errors more specifically.