What type of Bridges for All-on-Four Dental Implants?

Generally speaking, zirconium arches are much stronger than anything else, so from a durability standpoint that is a better option. However, during function, there can be a "clank" sound/feel if both arches are zirconium so sometimes the lower arch is a PMMA instead. This usually has a metal frame to add strength but the material will wear out sooner than the zirconium, so there should be a plan or budget for future costs. Zirconia is generally designed thinner than PMMA and is more esthetic, but some labs can do amazing things with each material.

The all on 4 dental implant treatment protocol involves the placement of 4 dental implants along with a screw retained hybrid prosthesis (bridge). In most cases this is PMMA as it is light weight, economical and provides adequate aesthetics and masticatory efficiency. 
Individual variations are always there and we do sometimes use hybrid PFM or Zirconia bridges as well.

The material used for the fabrication of the all on four restoration depends on many factors. The location/size of implants placed amount if vertical space available for the restoration and the type of attachment to the implants. So it would vary from case to case. So speak to your dentist about what's best for you. Zirconium is harder than PMMA. But harder is not always better.