I have never pulled anything larger than a H1 over soldier summit, but it is NOT hard to drive at all. The windy roads south of the summit into Helper/Price are the problem.
Soldier summit is 7477 feet. American Fork is around 4500 feet and Price is 5600 feet. So there is no large climb going in either direction.
And if you have a dog, the first rest area going south on Hwy 6, actually has an enclosed dog area; like a miniature dog park.
Having lived in Moab, and 90 percent of the time camping in ID, MT or WY, I have traveled it many times. And I have traveled both routes.
Hwy 6 is by far faster and very scenic; however, going south on 15 to Hwy 50 over to Salina, and then jump on I70 is only about 45 minutes longer. And that trip on Eastbound 70 takes you through the San Rafael Swell and talk about some fantastic scenery.
Also, if going via I70, make sure you can travel about 119 miles from Salina to Green River; nothing in between but scenery.