Here's what Chip Deffaa wrote in the Mississippi Rag in 1989 after talking to Challis:
"(...) Challis did a couple of charts for Glenn Miller, too. "But by that time, Glenn didn't like Bix," Challis says. For Miller looked over the charts Challis had prepared and said something to the effect that Challis seemed to be trying for a Bixian effect, and today's kids didn't know who Bix was. Miller had no interest."
Like most arrangers, Challis knew perfectly well how to write commercially. And as with most arrangers, his heart wasn't in it (I've got a printed chart of "Lullaby In Boogie" by Gil Evans; it's commercial crap, and Evans must have known it, but on he went to work with Miles Davis).
Miller and Challis had started their arranging careers simultaneously; in 1926 Challis started writing for Goldkette straight out of college, and in less than a year had been signed up by Whiteman; in the same year Miller started with Pollack (ironically attempting to emulate the Whiteman sound). Interestingly, both Challis and Miller studied the highly mathematical Schillinger system in the 1930s. What it did for them, I'm not sure.
About Challis "reaching his musical peak" a decade earlier: he certainly hadn't been more prolific since his Whiteman days, but logically arrangers only get more proficient with time; both Miller and Challis would have been well aware of this. It sounds to me like Miller had this alpha male thing with Challis, as he did with his other arrangers (read Gene Lees' interview with Billy May in "Arranging The Score" for more on this).