Multiple implementations of the consensus logic will lead to forks eventually.  One of the two is bound to become inconsistent with the other at some point and this will result in a fork.  The presence of forks (or the possibility of presence of forks) reduces the security of bitcoin as you have to be careful when you receive money as you need to be very sure that you've received money on the right fork and/or that there is no fork.

How long the forks last depend on the nature of the difference, popularity of the clients and probably the reaction times of the miners as well.