Warzone is better

They're both pretty terrible considering their AAA games.

Audio: Warzone audio feels like the person in charge of it spent the entire budjet on the airstrike sound effects (You know that horrible screeching carpet bomb noize that makes it so you hear nothing for a few seconds and have to shout over the mic for people to hear you)  and as a result of this audio design people can drop in on you or sprint up to you without you even hearing them, it really is abysmal sound design. I thought Apex's audio was pretty bad but Activision just outdid Respawn on that front.

Servers: Both pretty terrible but warzone really does have me scratching my head if i'm playing on 12 tick servers at some points, getting shot at just as you go beyond corners and able to shoot people as they're going behind corners, the whole peakers advantage, one of the worst Call of Duty games in the series when it comes to their servers.

I will say though Activision are far better than EA/Respawn because they actually update their game with significant meaningful content unlike Respawn who just continuously and shamelessly try to milk this game for all its worth. It took Activision a week to add solos, Respawn are still debating on weather it would sell more skins in a limited time solos event than add it full time which is absolutely pathetic.

Also Warzone feels more balanced than Apex, premades in Apex stomping random/solo players isn't balanced it's an unfair advantage... it makes me laugh when Respawn go on about the integrity of ranked when the game favors premades.