So much depends on your rig and your experience, I'll add that as a proviso.
You don't say what you are towing and what you are towing with. A fiver behind a diesel dually is one thing, and an R-Pod behind a half-ton is quite another.
Assuming you have a decently matched pair, and assuming that you aren't in a hurry, the scenic routes are infinitely better, and the roads are all adequate for semis ... to say nothing of an RV.
Here's the deal. You need to become proficient with manual shifting of your transmission. You'll crest several mountain passes over 11,000 feet en route, and you absolutely MUST be capable of using lower gears to control speed on the downhills. If not, you'll smoke your brakes in no time. If you have a diesel, you MUST have an exhaust brake. These hold true regardless of route, but you can't avoid these tactics on the "back roads."
On Rt. 9, on your way into Breck, you'll descend
Hoosier Pass, and it starts at just over 11,500 feet and drops to 9600 feet. The link shows several switchbacks en route. It's not a problem if you can save your brakes and use engine braking for most of your speed control.
If that's not your bag, stick to I-25, C-470, and I-70...but there's no free lunch out here. I 70 crosses the Continental Divide at Loveland Pass (Eisenhower Tunnel) at 11,013 feet. The downhill is a bit gentler, but just as much of a drop, because the "bottom of the hill" is at 9000 feet.
The image is of Wolf Creek Pass, but one's about the same as the other out here. I've been up and over most of them while towing, and manual shifting is the key to a comfortable drive.