A shorter (faster) exposure is better for capturing moving objects with less blur regardless of light level, but if you add low light into that equation then you're fighting video noise at the expense of lower blur. Low blur with huge grains is just as bad on a moving target as high blur for a moving target when the background is nice and crisp. With the exposure speed set to an acceptable level of graininess, you just have to hope that your target slows down enough to reduce the blurring that the longer exposure gives you. A long exposure would work fine if they'd just stop in place once for a good crisp face shot with no grain. Good luck on that one, especially if they're just walking or running through the scene. Shortening the exposure broadens that opportunity for them to slow down enough for an acceptable level of blur but might just make the best possible mugshot miserable because you've lost the picture quality completely from too fast an exposure or, looking at it the other way, expecting too much from your camera without providing it enough light to do its job. Even a cheap camera works fine with proper planning (control the angle, know the distance, use the right lens, and provide enough light). Better cameras just allow the installer to broaden the effectiveness of a single camera.
Everything else being equal (it rarely is), it's easier to light up 1 million pixels on a sensor of a given size than 2 million on the same sized sensor, so theoretically you'd get less noise and be able to speed up the exposure (thus cutting down the number of photons per unit of time) for less blur with a 1MP sensor than a 2MP because twice as many photons are hitting each pixel and trying to light it up. You could always have a lousy insensitive 1/3" 1MP sensor pitted against a fantastic 1/3" 2MP sensor and have the 2MP one win easily. Lux ratings are the best way for a consumer to judge this in combination with other things like the installed lens but as far as I've ever heard there are no standardized tests between companies even if they decided not to lie or fudge things a bit.