Does one big pixel produce a better (whatever "better" is, I think the major criteria being less noisy) than several small pixels grouped together having size of one big pixel?
You'll find pixel bucketing used when DSLRs do video... the combine groups of sensor pixels into a single RGB pixel. Is it better than one big pixel? For light gathering, no... that one big pixel would have more area devoted to the photodiode. On the other hand, for DSLRs, since you're a single-chip system, combining, say, 9 chip pixels per video pixel is better than just using individuals. For one, you can average pixels, which helps to eliminate the effect of low level random noise. Secondly, they get unique per-pixel color.
Because while the difference in resolution between, say the HMC40 and the HV20 is in favor of the HMC40, it is not THAT huge. The HV has about 3 Mpix with 1/2.7-inch sensor, the HMC has 9 Mpix on a 1/4-inch sensor, and the difference in resolution is only about 50 lines. Is it worth to have so many pixels, especially in this price class?
The HMC40 actually has three 1/4" sensors, each of which is 3.05Mpixels in size. Like most camera sensors, this is a 4:3 sensor, so when you shoot video, it's cropped to 16:9. And you have three sensor samples per pixel. That's also an improvement, both in color and light gathering. Basically, when you send light into a 3-Chip camera, other than a tiny loss in the diachroic prism, all of the light entering the camera hits a sensor, 1/3 of that light on each chip. For a single chip camera, you have a Bayer Pattern (or similar) filter array, so only 1/3 of the light entering the camera is reaching a sensor (some single sensors include a luma-only pixel in the array, to increase sensitivity).
Also, is there a formula to calculate comparative light sensitivity of a single-chip system vs. multi-chip? Does a 3-chip system deliver more light, or is it actually less light because of losses in the prizm?
Losses in the prism are there, technically, but small enough to be negligable. You're losing 2/3 of the light hitting a conventional Bayer sensor through filtering, though some more recent sensors use RGBW patterns (W = white) to boost luma. So basically, the three chips add up to full illumination in a 3-chip camera, 1/3 illumination in a single chipper. So you need 3x the sensor area in a single chipper for the same light sensitivity as a 3-chipper.. which does tend to make sense. And of course, this will vary by technology, too.