Yep. Again, the advantage of larger tippet is that it turns over easier. Easier to cast, more accurate, and doesn't twist the heck out of it. Plus higher strength for fighting fish. The advantage of thinner tippet is that it helps prevent drag (water pulling on line which pulls on fly).
It ends up being a function of the fly size. Larger flies are harder to turn over and have less drag issues, so you use bigger diameter tippet. Smaller flies are easier to turn over and have more problems with drag, so you use finer tippet.
My rule of thumb is fly size divided by 4 plus 1. So a size 8 is 3x. A size 12 is 4X. A size 16 is 5x. A size 20 is 6x.
Tweener sizes you can go either way, depending what you deem your greatest issue at the moment is. This is "fine tuning".
To take it further, you can also use other methods of fine tuning. Lengthening the tippet reduces drag and makes it harder to turnover, so it has the effect of going finer by a half size or so. Same with fluoro vs. mono, the fluoro is stiffer, so 6x fluoro may act like 5x mono, for instance.
Multiple ways to skin a cat. The important thing is to recognize your issue of the moment. Are you having trouble with accuracy? Getting it under a limb? Fish breaking off? Any of these would move you towards thicker tippets (lower X number), shorter tippets, or stiffer tippets. If, on the other hand, you're struggling with drag and getting refusals, go the other way. Finer tippets (higher X number), lengthen it, or go to softer tippet.
I generally refuse to go finer than 6x for moral reasons (lengthens the fight and causes breakoffs). Lengthening a 6X tippet with the softest mono I can find and making some casting adjustments, and I can generally minimize drag effectively enough down to a fly of size 26 or so. I don't go any smaller than that.