Assume you mean microfibre rather than fleece? Fleece isn't absorbent at all, hence is used for 'stay-dry' liners and for wraps.
Microfibre is pretty good but, in my experience, usually ends up smelling like wet dog after a bit.
If you need something that will dry quickly and be easy to use for nursery, how about BumGenius BTP pockets? They are by no means my favourite of my fluff but I find they are ruddy reliable. Being pockets you don't have the faff of two-parters so they are pretty idiot nursery-proof. And they come with microfibre inserts so very quick to dry.
No good for nights in my experience though I hear some people use them overnight successfully.
Microfibre are great for a couple of hours in the day, but no good at all for long periods or nights - they leak without fail! I only use them when I am expecting him to poo so don't need to absorbancy.
I second the pockets - esp Bum Genius - very good and dry well.
I had one microfibre Little lambs and needed more nappies but I bought cotton instead. Good compromise for day times - still dry in one day on the line but lasts longer than miscrofibre. Would still go for bamboo at nights though - although my LO can use Bum Genius as he doesn't wee much.