Imagine you are looking at an 8.5 x 11 page on the 1600 x 1200 screen .... now you change resolutions to 1368 x 768, and you can only see 9.4" x 5'4" of the page. Basically, you can only fit 55% of the information on the screen at the same relative size. I use 1920 x 1080 on laptops of 15" and 17" size
Images will be sharper on a higher resolution screen, though the computer will need to be more powerful to push the increase in pixels. With this small disparity though it should be barely noticable. I'd definitely recommend the higher rez display, if only because viewing webpages, images, and pretty much anything will be a much less awkward affair.
Not only are the comments regarding clarity (sharper image) and more windows displayed correct, But also the higher resolution panels are HIGHER quality than the lower resolution panels. HOWERVER the 1600 x 1200 panel will be much more expensive.
Some additional comments
Aspect ratio: 1600 x 1200 is a 16:10 so More square inches than a 16:9 display given the same diagonal measurements.
For 15" laptops the 16:9 (1366 x 768 or 1920 x 1080) is far more common than than 1600 x 1200. 1600 x 1200 is more for High res 10" tablets and the 14" and smaller laptops. For 15+ in laptops and you want the better panel with high resolution look for 1920 x 1080.