I just started a trip report for that area. We were out there last April.
I rode Lockhart on my KTM 530 EXC. Personally, I would not take anything over a 650 on that road. Most of it is not bad, but there were some short sections that were quite technical and could be a real handful on a bigger bike if you are not a better than average dirt rider. We did it from South to North. The most difficult section is on the North end and there are tons of pictures and descriptions of it on the net.
Typical road surface for most of the route
Just a barbed wire gate across the road!!
About 75 yards of steps and ledges heading down into a wash
One of the short challenges, but doable if you are careful
The start of the longest challenge on the North end - basically a BIG wash ravine
Middle of it
End of it
We also did White Rim. Again, the majority of it is not bad. There are some sections on the NW corner near the Green river with some very deep sand and it goes for a few miles. If you don't like sand, this section could be a deal breaker. It is also a long ride. You will need a bare minimum range of 150 miles with nothing to spare. If you can't do that, I strongly suggest carrying a few extra gallons. Also, run it counter clockwise. This way you hit the sand section early while you are still fresh and not at the end when you are tired.
Part of the sand section on White Rim
There are a few sections with fairly steep and somewhat rocky climbs, but they are generally not long. Of course, if it is raining on ANY part of the route, things could get REAL ugly in a hurry.
Shafer Rd up to the Island In The Sky overlook is awesome and easily done on your bikes.
I've attached my track file. There are six routes. We did three on our big bikes (3 1200GSs and a KTM 690 Enduro) and three on the small bikes (KTM 450/530/690 and a DRZ400).
The big bike routes were GrandJunction, LakePowell SW, and Million Dollar Highway. Grand Junction and Million Dollar Highway were all pavement. However, the first 75 miles of the Lake Powell SW route from Blanding to the Hite Marina were absolutely awesome routes for the big bikes!! That is the Northern part of the loop. All of the rest is paved with two exceptions, Mokee Dugway and Comb Wash Rd (DEEP sand!!). Originally, we had planned to run Valley of the Gods after dropping down from Mokee Dugway, but it was raining pretty good at the time and we did not want to risk any nasty mud with the tires we had (Heidenau K60s on my bike). Comb Wash was fantastic, but there was a pretty long stretch of seriously deep sand/silt. I made it through without dropping the GS, but it was a wild ride!
Sand/gravel mix that was fun and ran for some time
Nice stretch of woods as well
Some red dirt/sand along the way
Some rocky sections as we dropped down out of the mountains
Fairly firm part of sand section where it was safe to stop and restart on Comb Wash Rd.
The small bike routes were White Rim, Lockhart, and Sweet Alice. Of those, I would consider Sweet Alice to be big bike friendly with a few small exceptions. I would have been fine on my 1200 GS for most of it. If you look at the far West edge of that route, you will see that we turned left on Left Leg road. This was a non maintained two track trail that was pretty rough. I don't think I'd take a bigger bike down that one. In the center of the route you will see a loop. DO NOT take the big bike down the Northern part of that loop. It is a washed out cow trail. The guys were ragging me pretty hard when we were heading down that one and questioning if I knew where I was going
Of course, I did
Lastly, there is that leg that runs North just to the East of that loop. Going out it wasn't too bad, just a little sand here and there. However, it brings you to a set of switchbacks that should be named Mutiny Ridge because that is where the guys really questioned my sanity. I got down to the third switchback and stopped. They stopped at the first. There were probably four or five more below me. It was VERY steep and rocky. It was quite challenging even on the 530.
Much of Sweet Alice is like these
This is the switchback where I stopped and the others walked down to me.
It is always hard to gauge how a road will be from the responses of other riders because of the WIDE range of rider skill and its impact on impressions of how easy or hard a road may be. There are riders that do roads like Lockhart on 1200GSs and the big KTMs, and some would likely consider it not to be a hard ride. I could probably do it as well, but it would take a LOT more effort and energy than doing it on my KTM 530. As such, the risk of injury to the rider and damage to the bike goes up accordingly. Also, the suspension on the 1200 would make for a rougher ride than that of the 530, which over a 100 miles or more would really start to wear me down.
Just as a reference, all the trail guides and maps I bought before our trip list Lockhart as a difficult/expert route. I think the White Rim was rated as moderate to difficult. You can drive most of Sweet Alice in a car, but it would be a bumpy ride. In fact, we met two trucks pretty far to the West side of the route that were hauling cattle trailers and heading back in toward Blanding as we were heading out. They were going slow though. Other than that, we had the road to ourselves the entire day. Come to think of it, we had Lockhart and the Lake Powell routes all to ourselves as well.
Welcome to the Two Wheeled Texans community! 
Feel free to hang out and lurk as long as you like. However, we would like to encourage you to 
