Mulch is sawdust, and sawdust is mulch
Thing is with sawdust is it's really high in
carbon,
and if it gets into the soil, the little guys down there will use loads of nitrogen breaking it down.
Not the end of the world, but unless you add huge amounts of nitrogen (
urine springs to mind...)your plants will most probably be yellow and sad for quite a while.
I don't use wood-based mulches on annual garden beds as I'd dig it in, but anywhere else, I go nuts!
Trees love the fungal environment that woody mulch encourages.