Mark, some chipper shredders have different screens as an option. So, for very green material you’d use a more open screen to alleviate clogging. For allotment type use I think a hammer/small axe is quite sufficient.
However, with a few acres to tend, I’ve just bought an Eliet Maestro which is a reasonably chunky petrol engined machine and find that mixing the green in with branches works ok.
The downside of the m/c, for most people, is the noise and if you have neighbours, you’d be most unpopular.
The big plus is the fantastic compost material that heats up very quickly and must destroy any weed seeds (& any good bug life). The plan is that the hot compost plus cold compost from general greenery will make my garden self sufficient without the tons of cow manure usually spread.
Plus it controls the amount of woody waste piles we accumulate otherwise.
PS We don’t have neighbours!