The reason I opted for having Qui-Gon be supervising the trials as opposed to them both being Jedi Knights is because of the many, many instances of Obi-Wan referring to Qui-Gon as "master". There's too many to cut out, and if they're both Jedi Knights it doesn't make sense for him to be addressing Qui-Gon that way.

By making Qui-Gon a Jedi Knight overseeing the trials it allows for Yoda to be Obi-Wan's actual master and gives us a reason why Obi-Wan refers to Qui-Gon as Master. It also ties in to the line "Don't center on your anxiety Obi-Wan..." which can now be inferred to mean Qui-Gon believes Obi is feeling anxiety over his trials.