Mulholland had this to say in the October 1937 Sphinx:
Speaking of magazines of magic The Sphinx congratulates the Genii upon starting its second volume. The Wright and Larsen material itself is well worth the price of the magazine. Grandpa Sphinx is proud of the youngster.
Later, in the February 1938 Sphinx, Mulholland printed the following:
TWO EDITORS MEET
Recently we met, to our mutual pleasure and advantage. We found that some of our ideas were divergent. However, we discovered that on basic points we agreed. We cut our cloth the same, and merely use different trimming around the edges. We were pleased to find we possessed identical standards for magic and we feel others might be interested.
One : Magic is an Art and should be kept upon a dignified plane.
Two : Professional magic is a dignified vocation and its practitioners should have an high regard for the Art and a high standard of business ethics. Our definition of a professional is one who earns his living in whole or in part by the practice of magic.
Three: Magic is honored by enlightened amateur followers such as few other arts or sciences possess. However, amateurs should be precisely as careful to follow ethics as though they were profesionals.
Four: Magic as entertainment exists only for so long as the audience is mystified. This being true, tricks must be adequately rehearsed; ethical magicians will respect the rights of other magicians to original tricks, patter and routines. No ethical magician will countenance exposing of secrets of magic. A definition, to which we agree, as to what constitutes exposing is: "an expose of magic consists in divulging, indiscriminately, to an uninquiring public, by any means whatsoever, the secret workings by which tricks are accomplished."
The above, basically, is our code, to which we as individuals subscribe. Moreover, this is the policy which we have always had, and will continue to have, in the editing of our respective magazines.
William W. Larsen, Editor Genii
John Mulholland, Editor The Sphinx
So, it doesn't sound like there was any animosity between the two at that time, though I don't know if anything happened later on.