New PC monitor

Running at native resolution gets the most out of your system so given two monitors the same size but different native resolutions I would expect higher frame rates on the monitor running at native resolution rather than windowed.

In extended mode, the monitors don't have to be run at the same resolution. You can run each monitor at their native resolution.
Running at something other than native resolution: I don't know if there are performance effects, but there are definitely visual effects - similar to what happens when you rescale an image. This link gives a good overview (at least, better than I can explain) of why this is: http://www.cambridgeincolour.com/tutorials/image-interpolation.htm

Curtis
 
I do not recommend HDMI for anything above 1080P due to bandwidth limitation issues that will cut refresh rates beyond 1080P. 60Hz is satisfactory at 1080P but beyond this resolution the refresh rate will be cut to 30Hz which will have a negative impact on the viewing experience.

HDMI 1.3 (which should be on anything built in the last few years) and later support up to 2560x1440 at up to 75Hz. For 4K at 60Hz, though, you'll need either Display Port or HDMI 2.0 (and I don't know if HDMI 2.0 is readily available yet).
 
HDMI 1.3 (which should be on anything built in the last few years) and later support up to 2560x1440 at up to 75Hz. For 4K at 60Hz, though, you'll need either Display Port or HDMI 2.0 (and I don't know if HDMI 2.0 is readily available yet).

There are also issues too with some video cars not supporting the new 4K resolution. The are capable of the resolution, but do not display on the new monitors.
 
Running at native resolution gets the most out of your system so given two monitors the same size but different native resolutions I would expect higher frame rates on the monitor running at native resolution rather than windowed.

Cheerio John

Running a 3D application at anything lower than your monitors native resolution should always improve frame rates. The same monitor in either 1080P or 720P will provide a higher frame rates at 720P considering the GPU has less data to process due to the lower pixel count.

The obvious trade off is image quality. An acceptable frame rate and visual fidelity is a balancing act.
 
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