The "large pixels" school of thought is based on the fact that the larger pixels will actually hold more electrons ("well capacity") and therefore gives you potentially more dynamic range after digitization. They don't actually gather more light - that's entirely a function of the solid angle captured by the lens, and the physical aperture size of said lens. It's like a bucket under a hose - if you put an obstruction over both a large bucket and a small bucket with the same size hole cut in it, the larger bucket will get the same amount of water in the same amount of time, but it will hold more water given a longer "exposure". As Jake notes above, Canon's larger (older) pixels are less efficient at light gathering due to the physical design, so they don't even capture as much light as should be possible.
The real goal is to put as much light onto the pixel site as possible, which means a longer lens and/or a larger physical aperture. I've done informal tests with my 7D (2009) and my 5D3 (2012), and by putting the same number of pixels on the target and giving the sensor as much light as possible (ETTR with the 7D to fill the pixels as much as feasible) I got images that were hard to differentiate visually. In practice, users tend to underexpose the images to avoid blowing out the highlights, and the small pixel sensors don't fare so well (fewer values to digitize) in that situation. The fact of the matter is that we do not subconsciously take this into account (I'm guilty of it myself) and the larger pixels give us more exposure latitude in situations where we don't have time to obsess over exposure.
The 7D mk II is actually a newer, better sensor than the 1Dx; if it had similar electronics internally, the image quality would be even closer than it is (there are numerous reasons why the 1Dx costs 4x as much). Even now, the thermal noise and banding of the 7D2 are better than the 1Dx - which is important if you're taking low light exposures or stacking as in astrophotography. Again, the 1Dx larger pixels are more forgiving, but if you stress both sensors to the limit the 7D2 acquits itself very well.
Here
is a good analysis of the 7D mk II with comparisons to the 1Dx and 6D sensors. Used properly, it's an amazing camera; the strengths of the 1Dx go far beyond mere sensor differences though, so don't take this as in any way disparaging of the Canon flagship.