Although the question of sleeping on one's back or side may indicate a choice direction, gathered-end or bridge, note that usually the way someone sleeps on a bed does not always (or maybe not often), translate to how they will sleep in a hammock. In a bed, pressure points are built up around the hips and shoulders. It is a different environment from the support given when in a hammock.
I assume that side sleepers gravitate to a bridge hammock because it is more familiar, more bed-like. It's too bad there aren't more opportunities for someone to try both, or try hammocks that are in their preferred size range.
One occurring issue with a hammock, GE, or Bridge is called shoulder squeeze. If a person has wide-ish shoulders, and the GE or Bridge isn't wide enough, this squeeze might be felt. If I were a big fella or gal, I'd pay attention to the width of a GE or the width at the head end of a bridge hammock. One vendor who has a unique design - the spreader bars aren't at the very ends of his bridge hammocks, is Bill Townsand - see
https://thisgearsforyou.com
His design requires a bit more setup time for the first few times. However, after gaining some experience, an easy routine is established.