The graphics card can support all different kinds of resolutions, you know? It doesn't JUST deliver 1920x1080, and if your monitor is insufficient it wont work?
The GTX560 is a better card, not for the monitor but for the computer. If you are wanting to pick a graphics card based on the monitor you are using, you are doing something very, very wrong. The graphics card (GTX560) costs double the price of that monitor, so why would you want to base your choice on the less-than-ideal piece of hardware?
My advice: Get the GTX560. It's newer, cooler and more powerful than the GTX460, and it will last you longer. GTX560 is the best for you between the two.