Take Cover is slightly slower than Crouch as it does several things in series
What is the difference between Crouch and Take Cover. Doesn't both Crouch and Take Cover either drop you into the shield cover or move you behind real cover?
(1) Validate your selected hard cover spot with the server.
(2) Roll you into any selected spot / slide into selected spot if close
if that fails
So, at the minimum, Take Cover will add client server latency on top of your personal reaction time and default ability activation latency.
Both abilities offer the same benefit: If an object interrupts line of sight between you and an enemy, you gain cover benefits against the enemy.
For PvP specifically, where you need precise control of your character, I really recommend using Crouch (default: shift-f) over Take Cover. There's definitely cases where Take Cover is very useful (you can bridge large distances by rolling into cover), but when faced with fast moving enemies that know how to play line of sight or obstacles like The Pit's fires, you're better off and faster using Crouch. It may take a little bit to get used to using both effectively, but it definitely helps.