I've used both styles ,walkbehinds and PTO driven, and prefer fwd turning as it's not fightin the tractor to go ahead.
What truly helps BIG time, is to ALWAYS add 'soil amendments' EVERY year ! Pony poop/shavings, grass clippings, leaf compost, kitchen waste, dead veggie s, potted plant remains, peatmoss,top soil, everything organic should go back into the garden. You can't add enough. I 'top dress' about 120-160 cuyds of composted ponypoop/shavings ( stable sweepings) every spring on wife's 1/3 ac garden. Also add all the grass clippings(pure nitrogen) and leaves but NOT black walnut !! There's a poison in them, kills toms and peps !!
With gardening you get what you give, so the more compost in the more veggies you get !