I think you got a couple options when it involves garden and compost:
If not want to chip, maybe consider
Hugelkultur is a marvelous way to use deadwood and create a rich garden bed that sustains your plants for years. Here's what to know.
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If chipping, maybe consider you need to compost the chips first so as not to steal the nitrogen from the soil. (Some grass clippings may help speed up the process
if plan to burn the pile, when it makes sense is to burn the pile over the garden the spread the ash(yes, that would mean wait with the burn until garden finished for season)
personally I think anything you can put back to the permaculture is a win. i ve had good luck with any of the above, but i really like framing a raised bed and filling with the logs/branches and then backfill on top with compost (sort of combines all the above for something that continues to produce - ime the downside is it settles more than expected, but chickens do the backfilling

)). Makes for very nutrient rich soil that continues to break down. Sure it’s more work, but also it’s fertilizer priced right
Anyway I think this is a dealers choice between effort and concern for controlled burn.
I have a chipper and love it and would buy it again. Downside here is frequency of use is low.
Good luck.