I have installed an ssd in my PS4 pro and games like Destiny 2 and The Division 2 run a lot faster, load quicker, etc. 

However playing the Black Desert Beta, it runs extremely choppy with frame rate drops  

I then tested my brothers PS4 Pro WITHOUT an ssd and it ran a lot smoother. 

Why is the game running worst with an ssd?

I have SSD installed (Toshiba) and the game running smooth 

Works fine with my Samsung ssd. 

same issue as OP, i also made a post about it. Game worked fine for aug 20-aug 22 before the "official launch." As soon as the servers filled up the frame rates dropped to unplayable levels.

However, as you stated, the graphics are choppy and have been "pixely" and very low quality even beginning on Aug 20. 

I was assured during the beta from GM's and CM's that it is a beta and not meant to be a finished product. And that i should understand FPS drop and mid level graphics should be expected. Fast forward to paying $100 for what i assumed was a finished game (minus the coming DLC) and you can imagine how disappointed I am.