A charge will always have an attack target, so you can't argue that the charger can change his target to the counter charger (it's right there in the Attack & Defenses section that talks about Attack). So then... what happens? How about moving both the charger and counter charger simultaneously?
Say PC charged over the line, the enemy's readied action is triggered, so both of them will move one space at a time (they are in effect, both moving. PC toward his target, counter-charger charging toward the moving PC) to create some scenarios.
Scenario 1
If the enemy reach the PC first (from any direction relative to the PC) before the PC reach his target, the PC is hit and his charge is nullified (his movement part of the charge is interrupted). Narrative term.
PC "I'm going to run you down!" focusing on his target
Counter-charger hits PC, effectively sends the PC off his run before he reach his intended target. "Oh no you don't!"
Scenario 2
If the enemy reach the PC first (from behind, or slightly behind the PC) before the PC reach his target, the PC is attacked and missed. The PC's charge will continue with no OA from the enemy since the enemy struck the PC with the charge attack on the same square that the OA would be triggered from (OA isn't a free action, and only free actions you can take as much as want at anyone time). So the PC parries/dodge the counter charger's attack and countinues with the charge.
Scenario 3
If the enemy reach the PC first (from the side or slight in front on the side) before the PC reach his target, the PC is missed. The PC must take an OA to continue the charge (since he will have to leave his next square which is also adjacent to the now stopped counter-charger). By the PHB, there is no reference referring to if the PC can choose to stop his charge or not to avoid the OA (hence I used the word "must")
Scenario 4
If the enemy reach the PC first (directly from the front) before the PC reach his target. The charge from the PC is automatically nullify since "zigzagging" is not a viable option since 1) There are "curved path" pursuit charges if the intended target is moving (this is used when an intercepting charge is not an option), but never a zigzag charge (that would be called a feint or a manuever, not a charge). 2) There are no any real or fictious battle that someone zigzags on a charge (weaving through the battlefield to reach a target is not a charge for the record

) as zigzaging simply removes the momentum you would get from running in a non-obstructed line, the main reason why the attack is called a charge in the first place.
But here's the tough part, what happens then? If we go by the book, the PC loses the charge (since his charge condition toward the target can't be fulfilled) and the counter-charger gets a free hit in. I would probably house rule it so that both the PC and the counter-charger do a Strength vs Strength roll, whoever have the higher gets a basic melee attack on the lower one (narratively speak, both charged, clashed, one got overpowered and left an opening open for a hit to come in, you can of course make it a lot more dramatic... with a lot more words.), this in effect stops the PC's charge.
Scenario 5
PC reach his target before the counter charger hits him. PC hit his target first, then the counter-charger will hit the PC (and hopefully in a flanking position

)