O.K. I thought I would show some results of practical observation. I picked two cameras that seemed to produce similar image quality, though their sensor size is vastly different . . . the Nikon V3 and the Sony A7s. Yes, the Nikon captures more pixels, but that is the point, isn't it? We're trying to see if there will be an advantage to more pixels packed closer together. I think this demonstrates it well.

ISO 200

ISO 800

ISO 3200
As we can see here, what is happening is the dramatic difference of added noise at higher ISO vs. with a small sensor. What happens to the image from the larger sensor is a much-less-dramatic change in "resolution" or ability to capture detail.
THIS exemplifies why large pixels are important, but primarily at high ISO rages, because other than that, we don't see a huge advantage to large pixels. The D800 proved that you can put 3 times as many pixels on a sensor, yet still get a greater dynamic range at ISO 200. The D700 did NOT have the same high dynamic range of the D800, so pixel size obviously has NOTHING to do with dynamic range at lower ISO ranges. Noise? Well, we can see what happens with small pixels in the noise department by the top image . . . there is practically no difference from the tiny pixels of the V3 sensor to the huge pixels of the Sony A7s sensor (at ISO 200).
So it is not until high ISO settings that we experience image degradation based on pixel (photo-site) size. Since I usually shoot at ISO 100 anyway, I don't see a reason to buy camera with a huge sensor or big photo-sites (pixels). For me, the advantage of the small APS-C sensor is the dominant factor.
Now for an even bigger difference:

Nikon D700 vs. point and shoot cameras.
I was really surprised to see the results of the D700 vs. point-and-shoot cameras at low ISO. Some of these cameras even have serious zoom capability. One is even waterproof (Nikon AW110). ALL these point-and-shoot cameras have tiny sensors - the largest is the sensor in the Canon, which is 1/1.7" size (much smaller than what the Sony RX100 series or Nikon 1 series cameras have in them).

ISO 200

ISO 800

ISO 3200
As we can see here, what is happening is the dramatic difference of added noise at higher ISO vs. with a small sensor. What happens to the image from the larger sensor is a much-less-dramatic change in "resolution" or ability to capture detail.
THIS exemplifies why large pixels are important, but primarily at high ISO rages, because other than that, we don't see a huge advantage to large pixels. The D800 proved that you can put 3 times as many pixels on a sensor, yet still get a greater dynamic range at ISO 200. The D700 did NOT have the same high dynamic range of the D800, so pixel size obviously has NOTHING to do with dynamic range at lower ISO ranges. Noise? Well, we can see what happens with small pixels in the noise department by the top image . . . there is practically no difference from the tiny pixels of the V3 sensor to the huge pixels of the Sony A7s sensor (at ISO 200).
So it is not until high ISO settings that we experience image degradation based on pixel (photo-site) size. Since I usually shoot at ISO 100 anyway, I don't see a reason to buy camera with a huge sensor or big photo-sites (pixels). For me, the advantage of the small APS-C sensor is the dominant factor.
Now for an even bigger difference:

Nikon D700 vs. point and shoot cameras.
I was really surprised to see the results of the D700 vs. point-and-shoot cameras at low ISO. Some of these cameras even have serious zoom capability. One is even waterproof (Nikon AW110). ALL these point-and-shoot cameras have tiny sensors - the largest is the sensor in the Canon, which is 1/1.7" size (much smaller than what the Sony RX100 series or Nikon 1 series cameras have in them).