Based on this and this, there are two ways it can be done.
While there's no "hard and fast" rules on this kind of event, I've found two sources that address similar events.
The question How are simultaneously-triggered Readied actions resolved? does address this in the highest voted answer (32 points, and the only positive answer).
The answer being that the creature with the highest initiative will "get the jump" on everything else and to utilize their enhanced reaction time to act before those with lesser reaction times.
In this instance, it would come down to whoever has the highest initiative acting first. Coincidentally, this is also the character who Readied first. Even in the event of a tied initiative, there are stated ways of determining who goes first in a draw (from comparing dex scores, to players deciding who goes first, down to random chance).
Even if your Wizards plan on casting at the same time, reaction (aka Initiative) is still a factor. Just because you say or think you have an infinitely accurate reaction time doesn't mean you do.
In a different question, What order do Opportunity Attacks that trigger simultaneously happen in?, the person who's turn it currently is decides in what order the triggers occur. Since these are readied actions that indicate that initiative (and turn order) has been decided, there will be a single character's turn who can decide. Better hope he's on your side.
Keep in mind, this is based on an optional rule listed in Xanathar's Guide to Everything, and your DM may have other plans for your "Reaction" time.
These two options are built off of either assumptions or optional rules, so the best source for a question like this is whatever your DM says. Considering events like this don't happen without DM's supervision, it's a reasonable assumption that he may have plans for how he wants to determine a contest of this nature.