Is this shower trap better than a P-Trap?
This is what is called a drum or barrel trap in North America. They used to be common many years ago. Then P-traps became available and were found to be preferable, leading to the banning of drum traps in model plumbing codes.

Unfortunately, I'm not privy to the reasons they were banned. Some disadvantages I see is they retain a relatively large amount of wastewater. In theory, some small portion could remain in the trap for quite a long time, possibly allowing mold, bacteria and other undesirable things to grow in there. P-traps, by nature, have more of a first in, first out sort of flow, minimizing the chance of old wastewater staying around. In the case of the shower and floor drains, the wastewater is in very close proximity to the drain grate. It makes it easy for occupants to come in contact with the wastewater, which would generally be considered an unsanitary event and thus frowned upon.

Floor drains in residential bathrooms are quite rare in the Northern and Western hemispheres, except where the floor drain also serves as a shower drain. I've seen such a configuration in mostly tropical and sub-tropical countries. Floor drains in commercial restrooms are so common, they might be required. I'm too lazy to check right now.

Floor drains in residential laundry rooms, while perhaps not common, are certainly seen often enough. Still, they are not required, so many laundries have none.