Knowing what your opponent is on is HUGE....in certain matches. If you are on blue and you are facing shops and know it, what are you going to do? Are you going to mulligan into your single hurkylls? Are you going to mull until you have 3 basic/fetch lands? if you do, you likely lose on mulls more than you win on luck-sacking into the perfect hand. Your best bet is to play that deck you are comfortable with, hope to make smart plays and minimize error, and win with any luck.
Now if you are on a certain deck running 1-strip/4-waste and perhaps even something like main sorcerous spyglass and KNOW your opponent is on dredge, you are damn straight mulling a good hand of 7 for a decent hand of 6 with waste/spyglass is a HUGE gain in game 1. It is the difference between a near auto-loss into a favorable g1 matchup. Even in a deck you are semi-comfortable with as opposed to a deck you've mastered, if you have ample cards against a deck that hinges on one axis and know you are facing that deck, you are much better off. The same could be said running a null rod-based deck vs PO storm. If you know that matchup is happening, you are better off mulling into the 1-of chalice or turn 1 rod off a mox than keeping a solid hand that won't win until turn 3 or stop artifacts.
If you have 3 basic land + an orchard, and an oath...you keep that vs shops. If you have that hand vs PO, you probably lose. If you have that same hand in your oath deck and also know you have FoWs and null rods, you probably mull that away instead of hoping to live to turn 3 with no answer to getting stormed out.
So, the answer to the question again is: it depends. Based on the matchup, the knowledge vs mastery can make a big difference.