OMV: -- has Docker plugin with Compose support (no need for sep. Docker GUI like Portainer) -- SMB shares are (somehow) more reliable on Win clients -- has more beginner friendly GUI and attitude, easier to share with other users -- batteries-included features like fail2ban + Wireguard
Cockpit: -- first class citizen on EL / Fedora distros -- Podman yes, Docker no - no Compose/Quadlet support -- killer features like VM managements and Terminal -- bugs with Samba
I currently use OMV for serving files over my local network (just for myself) and running a handful of Docker containers. It works fine but I don't use 90% of it's features.
OMV takes over your system - lots of "Auto-generated and maintained by OMV, do not touch" in system configs. By comparison, with Cockpit I could tweak and set up my own stuff. With OMV, when I needed to change my network settings, I had to fight bugs in the OMV GUI, and couldn't edit the configs directly. Same thing when I was trying to set up my disks in a particular way. This is a big issue because when something breaks, none of the general (non-OMV specific) answers on the forums help because you can't actually edit the configs...
The other is jank. I ran into many, many issues with OMV. Even for installing, I had to resort to 'curl .. | sudo bash' as the officially recommended option, with no proper uninstall method.