Pat Craig,
I probably agree with you on 6, 10, and 13 at Lawsonia. Those are my three favorites on the course as well, and probably my three favorite holes in Wisconsin. I think Lawsonia has the better par 5s and certainly the better par 3s, but Erin Hills wins for me with the par 4s.
You mention the repetition of elevated tees and greens around Erin Hills. I find the same sort of repetition with Lawsonia's countless dogleg right par 4s. The green angles on those holes keep Lawsonia interesting, but it does sometimes feel like hitting the same tee shot over and over again. I'm also not particularly enthralled with the stretch from 14-17, relatively speaking. They're good holes, but the course peaks a bit too early.
Erin Hills, to me, has the bolder and more varied collection of par 4s. The greens aren't as dramatic, but they're considerably faster which gives them much of the same movement. The distance variation is phenomenal. On my play at Erin Hills, I hit my approaches to par 4s with PW, 3I, 7I, 2I, 3w, 4I, 9I, 6I, SW, and 5I. Granted, I only hit the 2I, 9I, and 3w because of terribly mishit drives. But that's still a different club for every approach and pretty good variation.
Again, I'm splitting hairs as I love both and my preference is sometimes reversed, but I found Erin Hills to be the more interesting test. I also happened to be a 12 handicapper when I played it. I shot 92 and thought I couldn't play much better. A few days later I shot 77 on a different course and felt like I'd played slightly worse. It's certainly tough, but still enjoyable and far from unplayable. I played it with my 51 year old 30+ handicapper mother who also had a great time. She does prefer Lawsonia herself, but only slightly.
Can't argue on the walk though. It's a tough one.