How do you switch between your weapons on ANTHEM? You can hold two weapons at any one time, but the game doesn't make it incredibly obvious how to switch between them. Worry no longer, though, we have the answer.
How to Switch Between Weapons on ANTHEM on PS4
Once you have unlocked the ability to carry a second weapon and have one equipped at level 3, you can switch between your guns by holding the square button. This will automatically switch between the two you're holding at any time. It's simple, but the game doesn't do a particularly good job of teaching you it.