We're talking about monophase 32A 240V, right (yielding 7.6kW) using the UMC?
Wall Connectors can go beyond that (11kW), either one one phase (but 48A continuous!) or three phases (3*16A for a Model 3).
In continental Europe the UMC is severely limiting: we often have three phase 3*25-40A 240V coming into the house, and obviously it's easier to use 16A*3 240V for charging a Model 3 than to draw 32A from one single phase.
The earlier Model S/X UMC that supported 3 phase charging with an adapter to 3-phase CEE 17 sockets didn't have that limitation (but quite a scary adapter to the CEE 17 socket).
Either one safer than the other?
The wall connector is supposed to be used with a type EV or B RCD and that's safer, because it's upstream from the TWC (and fixed).
The UMC does detect even DC ground leaks (at least it was rumoured to do so, and it makes sense, since it's designed to be used on installations with Type A RCDs), but there is a theoretical danger that the UMC might get damaged (after all it's quite exposed) and make the operation of the Type A RCD that is upstream ineffective if there is an undetected DC leak (which would make whatever is on the same circuit less safe).
So yeah, anything that has things nicely mounted on the wall in a cabinet is safer than something that has vital electronics meant to protect you quite exposed. But in the US it's not so bad (although I don't like 32A going through a connector that has the UMC weight precariously hanging off it and which doesn't really have a locking mechanism, but that's just me).
A UMC is more hassle than a TWC with its own cable, though.