I'm not claiming to be an expert. I hope you hear from others who have used fleece, too.
I have MACHINE quilted with fleece - but just quilts that will be used and washed a lot. I don't think the quilted, pieced side looks as good with fleece as it does with batting. Fleece stretches, so I baste it with spray-basting to prevent the stretching as much as possible. I start quilting from the center to the outside. Inevitably, it stretches a bit, but it goes off the edges where it can be trimmed, instead of toward the center where it would cause puckers or pleats.
I think fleece may be harder to HAND quilt than batting. If I were you, I would test a sample before committing to hand quilting the whole quilt. I don't think fleece is a lot warmer than a quilt with batting, though it may be lighter weight. I use fleece because I don't have to fuss with 3 layers when I'm machine quilting :lol: I use batting when I've put a LOT of work into the top and I want it to look its best after being quilted.