I have a Vermeer 6"
chipper (BC 606) on a Kubota
L2900 (29pto ph, I think). The feed is hydraulic and adjustable from a barely perceptible crawl to a fast pull-in. The manufacturer recommends 30-60hp at the pto. I rented the same size
chipper and it had a 44hp diesel engine and automatic feed control; with 6" hardwoods the speed control would reduce the feed speed significantly to keep engine speed up.
6" pine will almost stall the 29hp tractor at the slowest feed speed. A 6" oak will stall it completely, so you have to feed it in by turning the feed on and off in short intervals; probably chipping 1/4 the time and resting 3/4 the time. That is no problem occasionally, but it really slows you down if you have a lot of large hardwood to chip; not only is the chipping slow, you have to hand control the feeder speed, so you can't be bringing another branch tot he
chipper.
Your
L4400 is probably about 50% more powerful that the
L2900 and your 9"
chipper is about 50% bigger, so I suspect you will have about the same experience on larger wood. If you don't expect to chip much hardwood in the 7 to 9" range, I would get the 9"
chipper and understand that it will be slow with the larger wood. However, if you plan to chip a lot of 7-9" hardwood, you will either go very slow, get a bigger tractor, or rent a 9" commercial
chipper with probably a 60hp engine.