You've hit a raw nerve on this topic. I definitely have experience and a personal bias......against anti-pill fleece and especially plush anti-pill fleece. Others say that they prefer anti-pill. Insofar as that goes, you will find more colors and patterns in the anti-pill type vs. the blizzard fleece that I prefer.
A bit of the back story: my cavies have always had fleece liners in their cage along with extra pads, cozies, etc. We always use towels for lap time as they can be tossed in the wash with detergent and bleach. Apparently, the softer types of fleece feel similar to towels to my cavies and they will pee & poop more in the cage with the softer variety. They know that it's o.k. to use the toilet on the towels during lap time and that transfers to the softer fleece. So........the cage gets far more soiled. Both my husband and I have noticed the difference in their behavior and the cleanliness of the cage.
OTOH, blizzard fleece is a thicker weave, more dense fabric which has the added advantage that it doesn't wrinkle or "bunch up" like the softer anti-pill variety. My sewn liners look far more professionally crafted and wear much better. Also, if you have a habit of using bleach, it isn't as damaging to the blizzard variety.
Once again, this is entirely a personal preference. I have been sewing fleece liners for ten years and have very strong opinions. You may have a different experience and we welcome your input.