From what I read here we should probably agree on "common semantics" here. Because I think I get what you're trying to say, but stuff like "better value" is very confusing because it's statistically untrue. You're however safer from anomalies the well, lower the number.
Basically it's like this (I'll just use saves but that's true for every dice roll in the game):
Going from 6+ down to 5+ to 4+ etc. your additional success value goes down with every step. 6+ to 5+ is a 50% gain in saves. 5+ to 4+ only 33% etc. So the first step is the most valuable in that regard (statistically speaking).
However, if you you come from the perspective of failure it's the other way round. The lower you get the less likely (percentage wise) it becomes to fail. 3+ to 2+ means 50% less failures. 4+ to 3+ you go from a 50% fail chance to a 33% chance to fail. 3+ to 2+ it's 33% to 17,5%.
So, while that looks like it's the same it's actually not. If you take variance into account and accept that you don't necessarily roll according to statistics you can stretch the odds quite a bit.
Rule of thumb is: The higher the number of dice the better it is to go for bigger successes. The lower the number of dice the more important it is to avoid failure. In combat & particularly with saves you also have to account for wounds but the general idea stays the same, it just gets another layer.