The higher your credit score, the better. If you ever had the choice of two different credit scores, you are always better off preferring the higher one.
However, while the utility of a higher score is always positive, it is not always large. Sometimes it may even be minuscule. Since having a higher score takes effort (and possibly money) it's not uncommon to end up in a situation where increasing your credit score isn't worth it, since the benefits are too little.
For example, in this answer it is claimed that:
there is no difference between a 750 score and an 850 score; you are already eligible for the best loan rates.
I was curious: What are the major breakpoints of credit scores where it does matter? Are there major score thresholds, that once you pass them, you suddenly experience tremendous noticeable benefits (like suddenly qualifying for a whole class of better credit)? Are there ranges of score (like the 750-850 asserted above) where, it doesn't really matter which part of the range you are in, you still enjoy the same benefits financially?