Chipper
As a general rule, tree surgeons tend to buy chippers because they are designed to deal with woody waste, like conifer, brushwood and cordwood. The chipper has blades, so you need to ensure that wood is as clean as possible and no sweepings should be added at the end of the job. The chipper produces a square chip which breaks down quite slowly - ideal for paths and top dressing.
Waste management, landscapers, grounds maintenance and hedging contractors tend to buy shredders because they pulverise with hammers all sorts of soggy, gritty, horrible material, like brambles, hawthorn, broken pallets, cardboard, food waste, turf etc. even drinks cans.
The shredder will produce a matchstick like product, which is designed to break down quickly for mulching and making compost.