RAW I believe both charms are in effect and the victim feels that both casters are their best friends and would defend either and take commands from either.
I don't have an electronic copy of BECMI Basic but I would go with the exact language of the edition you are using as they can vary a bit with slightly different sounding lines. RC commands to a charmed person it says should sound like suggestions from your best friend, for example, while B/X it is phrased as just any commands that do not cross the alignment or established habits or kill yourself lines.
The RC version also has a section talking about possible conflicts that can be a guide:
"A victim who is given conflicting orders and impressions by his old adventuring friends and his new "best friend" should react as any person would in real life: with confusion. He will not automatically assume that one party or the other is lying . . . even if the player wants him to."
Charm Person Range: 120'
Duration: See below
This spell can be used on any human, or human-like creature (such as bugbears, gnolls, gnomes, goblins, hobgoblins, kobolds, lizard men, ogres, pixies, or sprites). It will not affect undead, nor creatures larger than an ogre. If the victim fails to make a saving throw vs. Spells, the victim will believe that the spell caster is its "best friend" and will try to defend the caster against any threat (real or imagined). If the caster speaks a language that the charmed creature understands, commands may be given to the victim. Any commands given will usually be obeyed, except that orders against its nature (alignment and habits) may be resisted, and an order to kill itself will be refused. Creatures with above average intelligence (a score of 13-18) may make a new saving throw each day. Creatures with average intelligence (a score of 9-12, which includes the monsters listed above) may save again once per week, and creatures with below average intelligence (a score of 3-8) may save again once each month. (A charm may be removed by a dispel magic spell.)