1920x1080 is what we call "Full HD" and 2560x1600 is what we call "WQXGA".
It really depends on what you want to do, but in my opinion, going bigger is not a bad idea if you have the greens to do so. Just keep the quality of the Monitor in check so you don't get a terrible experience with colors and refresh rates.
So, at first glance, 2560x1600 is better.
Cheers!