Warzone does look big and diverse and probably has a lot going for it... except maybe the one thing that drew me to Apex in the first place: personality. I was never particularly interested in this kind of generic looking military shooter, and I doubt that -even leaving gameplay aside completely- it'll have anything to offer that'll be able to match my enthusiasm for the Apex cast and lore.
I still miiiight give this a try, if only because it's F2P and I'm curious about the experience. Never played a single Call of Duty game before (but then again I hadn't played any FPS title in well over a decade before Apex), and like with Fortnite it might be fun to take a look at another take on the BR genre. Like Fortnite, however, I don't suspect Warzone will have any chance to sway me away from Apex.
Only BR game that looks like it might have a chance to actually compete for my affections at some point is probably Spellbreak.
