Bridgeless suspension forks Suspension forks typically have a bridge which connects the two lower legs. In the past, this also provided a hanger for the rim brakes. I always thought though that the main purpose was to ensure that the two legs remained parallel in compression, so that there was no torsion on the front axle. 

I've noticed some MTB suspension forks that are bridgeless. In these systems what prevents the legs from compressing at different rates and twisting the axle? Can we broadly say a bridgeless suspension is weaker than a bridged one?
No, you can't broadly say "Bridged suspensions are stronger".  It's depends on many things, including the design of the system, materials used, build quality, etc.

As Batman mentioned, Cannondale's Lefty suspension is stronger than most traditional systems and isn't bridged, or even bridgeable.

Inverted, or "upside-down" systems, like the one in your photo, have other considerations as well, outlined in this question.  To your question, the thru axel keeps the stanchions bound together, preventing different rates of compression.

I think we will see fewer front forks with suspension bridges in the future and more inverted systems, as the technology trickles out to less expensive builds and the cost of manufacture drops.