Tour Divide is mostly roads, AZT is a trail.
The great divide mountain bike route basically parallels the Continental Divide hiking trail. It would be possible to do the same with the AZT.
Hard is all relative to ride the trail requires HAB "hike a bike" for every one. How much your walking depends on your skills. If you really want to ride the rideable sections then you want to do the HAB. If you just end up walking the bike more than riding you can always bail out to ride the road.
I use a mapping program called topofusion if you go here
http://www.bikepacking.net/routes/arizona-trail/ you can down load a network gpx file that shows the trail and the bypass options. With a bit of study you could create a custom route with less HAB.