I picked up a used Woods 7500 backhoe (7.5 foot dig depth) a couple of years ago for use with my NH TC33D. It was originally set up as a 3 pt hitch BH, but I got the new (at that time) Woods 4 point quick hitch subframe and switched it over to mount on that. (That subframe system is GREAT, by the way). I've been happy with the set-up, and finding it used saved me some $
My tractor is a little lighter than your JD 4400, but it handles the 7500 with ease. You might be able to handle the Woods 9000 on yours (9 foot dig depth). 
If you are going new, Woods has an updated line. Take a look at the BH70-X or the BH-80X. They've made a number of improvements (higher digging forces, etc.)
John Mc