1900 by 1200 versus 2560 by 1440 in different size monitors

Those numbers are the number of pixels & they are also the resolution. The first number is the number of pixels horizontally, the 2nd is the number of pixels in the Vertical. So you can just multiply the 2 numbers & get the total number of pixels.

The resolution stays the same for all sizes of displays. The pixel size of course is a bit larger on a larger display. So if you have a very large display & sit close to it, you may be able to see the pixel. This decreases the further away you sit from the display. So generally the smaller display should look sharper, but you also have to remember that the images will be smaller so things can be harder to see.

Rindi is correct. I just wanted to expand with one more thought. Pixel density (sometimes called Dots Per Inch, or dpi) is what creates a sharper image. So to answer your question, more pixels (i.e. better resolution) will look sharper on any size monitor... But the bigger the monitor, the less dpi... if the resolution does not change.