Price of these items on Antica:
Galea Mortis - 40kk
Gnome Helmet - 39.5kk
Falcon Circlet - 44kk - The most expensive item
I am owner of Falcon Circlet and basic on my experience I can say I prefer change it for Gnome Helmet. Reason is easy. Gnome helmet fit better on my hunting spawns. I usually hunt Falcon Paladins , Falcon Knights .
Falcon Circlet is good for spawns:
Kilmaresh Mountains with Priestess of the Wild Sun , Burning Gladiator ,
Ferumbras' Ascendant with Demons , Hellflayer , Grimeleech
Fire side of Library with Burning Book, Rage Squid ,Guardian of Tales , Ink Blob .
Galea Mortis is definitely good in pvp situations.
To sum up, the best for me is Gnome Helmet but it all depends on individual needs. In general Falcon Circlet gives you more options with hunting spots.