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I bought the Vertex Vent before I bought the Strato Vent. The Vertex uses the traditional hardhat design, basically suspends the plastic shell on webbing with an air gap in between, while the Strato has a foam liner between the head and outer shell. The Strato is only slightly lighter and has slightly smaller outside dimensions. It seems more comfortable than the Vertex when fully loaded (Vizir, Vizir protector, Nao+ headlamp), partly because the center of gravity is closer to the head so the eye shield doesn't shift around as much when moving around. The Strato Vent's foam layer may be hotter than the Vertex Vent in warm weather, though I have only been using the Strato in cold weather so I can't personally confirm this.
I did figure out how to make the Nao headlamp fit on the Strato when using the eye shield (same method should work on the Vertex). The shield covers the front headlamp tabs, but the headlamp stays in place fine if the headlamp cords are secured by the rear headlamp tabs and the lower bungee cord is routed underneath the circular EasyClip mount for the eye shield.
Petzl's Vizir protector is ultimately the feature that made me choose the Vertex/Strato over the Kask Zenith or Plasma. I am frequently work at night and prefer to flip the eye shield up when I don't need eye protection. The Vizir protective cover allows the headlamp to stay in place with the eye shield up and keeps sawdust, snow or rain from covering the lens when it is flipped up.
A few things to be aware of... it can be a bit unnerving to install the Vizir protective cover and even the Vizir itself because it feels like you are going to break something when removing the EasyClip mount covers and when snapping the protective cover into the hinge. Also, the Vizir was initially difficult to flip back down after rotating it up unless I was using both hands, one on each side tab. After using it for a few days, I can now flip the shield up and down with just one hand. Maybe it just needs a bit of break-in time or perhaps I didn't have it clicked in properly the first time.