well the difference between a 44 and 35 is very marginal but to each his own i myself if i had a choice would go with a 35 cause i wanna build a ttb lifted rig. now for the 9 inch i havent heard to much good about them i keep hearing to not use a 9 inch so i cant really help u on that but i heard its cause of the pinion but not sure. also do a search cause there are alot of threads on here pertaining to this.
The difference is that the D44 has a LOT of aftermarket support, IE hardened shafts, lockers, hubs, etc and the D35 has close to zero. The D35 is also physically huge because of all the TTB parts.
The Ford 9" is THE single best Ford factory axle to swap in. It's small, lightweight, bulletproof, has excellent aftermarket support, and is cheap. Anyone who will argue otherwise has no idea what they're talking about.
Full width looks badass but on the trails I think you will not be able to go places you could with something similar to what you have now. I would go with a D35 since it's a direct swap. And it's basically the same as a D44. Do the D35 and swap in some D44 knuckles and a 8.8 from an Explorer and you got a full size setup with RBV manuverability.
The D35 is great but it depends what you use it for. TTB stuff just has so many pieces that get hung up on rocks, tree roots, ruts etc where a solid axle would just slide through or over. As I said above, it also has very little aftermarket support...so if you spend a bunch of money buying the axle, gears, locker, brake parts, etc and end up breaking it all the time...it's still a waste of time.
This has been covered so many times it makes my brain bleed.
D35 = great daily driver axle
D44 and larger = great wheeling rig axle(s)
Period!