Tony Franklins Other Shoe said:
If I had a more consistent swing, playing the same ball would make a difference for me, but I really don't think it matters a whole lot unless you are a low handicap.
Focus on what works for you around the greens and how it feels off the putter if you are mid pack type of golfer.
Using the same ball every time has the biggest difference on your short game. Practice putting/chipping with the same ball consistently and you'll become familiar with how that make and model ball reacts around the green. The cover absolutely does change how the ball feels, spins, and reacts. At the very least, either play a surlyn cover OR a urethane cover ball during a round (e.g., don't pick a dirty, found Noodle out of your bag to drop after losing a new ProV1 out of bounds.) If you play premium balls, don't mix in a bunch of cheap balls in your bag, and vice versa.