>> For wood--I'm talking tree limbs and branches and woody shrubs and large stalks and the like--I use the chipper,
Anything thicker than my pinky finger I just throw behind some trees. THEY will stay there until they rot or I get around to sifting a little clay over them to help them stay moist so they rot faster. A chipper would totally be the right tool for that job, but waiting a few years for them to soften might enable the lawn mower to make more progress on them.
I only produce wood when I cut back or dig out the low-lying juniper
bushes that some landscaper planted as a no-care space filler. Mostly those branches are like woody vines up to a 1/4" diameter, but a few are larger. I chop them short with some old bolt cutters that I use like lopping shears, then try to shred with the (small, pretty quiet, electric) lawn mower.
With the dull old blade, on the twigs around or over 1/4", that's somewhere between inefficient and futile.
I gathered the chips after each pass and screened out the ones that were still too big and chopped them again.