The short answer is no. The same equipment won't give better results with video than it can with stills.
I think the apparent difference is due to exactly one thing: resolution. Try taking one of your still frames, resampling down so it's 1080 pixels tall, and then comparing.
There isn't any inherent low-light quality advantage in the way video is captured — in fact, it's really much more limited. But lower resolution hides many faults. Noise will be less apparent, but it also can hide motion blur — for example, from the longer shutter speed that you used for video.
Correspondingly, when inspected very closely, the still frames may seem bad, but if you actually make prints — especially relatively small 4×6" prints, but probably even larger ones — they'll look surprisingly good.