On Xbox One, voice chat is the only option. When you use voice chat with an attached headset, you will only be chatting with your team (or members of your Xbox party) during versus.
In the arena lobby you will be able to voice chat with everyone until the game starts.
Alternatively, there are comm icons you can use in battle. Check your controller settings on how to mark an enemy as a target or recruit. You can also mark terrain to avoid an area or recommend your partner to move to that spot.