From an operational point of few, here are some differences.
V2500 will go higher, sooner but may struggle the last bit - use V/S, it is better with the Airbus than speed, uses energy better.
Thrust off is different, the V2500 carries residual in the flare - this compounds the autoland differences - the 2 varients have different flap settings in Conf Full and as a result, the V2500 tends to float unless you close the thrustlevers earlier than on a CFM. Much prefer the CFM for autoland - more predictable.
CFM's start quicker - no waiting 50 secs for fuel on a hot start.
Don't forget your ignition on the CFM if weather is bad.
The engineers say the CFM is far more robust, stays on the wing longer but uses more oil - don't worry about regular top offs.
Summary - CFM is better all round
