The one on the right is relying on a strip of sealant, which should be butyl tape, not sure what that mess on the mockup is, to top water once that thin J channel fills up. The only water that will actually get in the valley is when the rain is heavy enough to completely fill the J channel.
Butyl sealant only works under compression, that is why end laps and z closures are usually fastened every 2 inches to get uniform compression. As it is the ends of the panels are not fastened in the valley or turned over. There will be no compression to seal against their sealant strip.
They are not showing any additional fasteners in that J-channel and it recesses in the valley metal turn up on the side. So what is holding the valley metal in place? What is holding that J channel in place?
If it is fastened in place it will leak since the J channel will fill with water and your roof is low enough slope that the water will run up the inside under the panel and when the sealant fails it will run up to the lip then under the j channel. When it comes down it will either get trapped if they are using some kind of adhesive to hold the j channel in place, or run over screws and cause a leak.
If there are no screws then the valley metal is only being held by the sealants they used to glue the pieces together, eventually the whole valley might slide down exposing the top.
In a heavy enough rain the valley could fill and water would either go back under the J-channel to any fasteners, or the j channel and valley could fill and go over the lip in the valley metal. Then your ice and water will be the only thing stopping a leak.
If there are no fasteners under the J-channel then the entire valley is relying solely on the bottom panel fasteners to resist wind uplift. Valley can experience significant uplift since a strong wind will be funneled up the valley.
The detail on the left is actually done wrong. As mentioned the fasteners in the Z closure should be every 2 inches, or at most every 4 inches to ensure compression. The valley is fastened so it can’t move and the panel will be turned over and hooked to the Z, and ideally a bead of sealant or rope caulk will be put on the top of the Z before the panel is turned over, mainly as a fail safe if for some reason water or snow can build up that high.
There are other details like the Berridge one that do not use sealants in valleys, which IMO are superior to using a Z in a valley. Some manufacturers make their valley so it has a flange or even tabs that come off the side to be fastened up higher than the panel where it is turned over and hooked into the valley metal. Some details also fasten the panel ends in the valleys.
I would not accept that detail on a project.