Having used a GH5, a GH5s, a Sony AX100 and a Sony Z90 (the "pro" equivalent of the AX700) underwater and being a video guy only, the setup that works best for me is a dedicated video cam, currently the Z90.
I am saying "for me" because what you choose wil depend on a lot of different factors. As you say, if you want to do phots as well as Video, you'd have ot go the hybrid route. Yes, the AX700 can shoot photos, but nothing to take really serious.
If you are a video guy and - like me - hate fiddling with lots of different lenses, ports, extension rings, focus and zoom gears (just to find out when you arrive at the other end of the world that you left important bits at home...), then go for a Gates/AX700 setup.
I just grab my housing before the dive and put it back on the deck after the dive and relax while my hybrid buddies are still spending another 30min+ configuring their rig for the next dive. Can be fun as well - but its just not for me. One battery takes you easily thru 3 dives.
Whatever you choose, with both setups (GH5 or AX700) you cant go completely wrong as both are great systems.
Just to mention: Yep, the specs in the GH5 look much more impressive. But you cant beat the super precise auto-focus on the AX700/Z90. The autofocus on the GH5 even after a quazillion of firmware updates remains to be a bit of a joke.
And also just to mention: If you a are "big sensor" freak: Forget both both GH5 and AX700 and go for a RED Monstro :-)) Joking aside, its a topic somewhat blown out of proportion IMHO. The 1'' Sensor in the Sony does a great job!