Actually it may drive down the cost of shipping. Competition is always a good thing.
Of course, us consumers think that.
The canal is currently at 100% capacity to my understanding, but Panama probably greatly enjoys that 100% capacity and the fact that there's no competition to drive down the X cost per ship-ton they charge to send a ship through the canal.
Panama would still remain the preferred canal since it's shorter and would have fewer locks, but if it costs half as much to go through Nicaragua and takes another 12-18 hours above whatever it takes to go through Panama... I can't help but think it would suck away at least some of the Panama traffic and also drive down rates for traversing.
And if they somehow increase the size of ships able to traverse (i.e. "Panamax" is smaller than "Nicamax") then Nicaragua would become the dominant choice as new ships are produced to fit the new locks.