There is no 'competition' from a new registry. EASA control European airspace full stop. To operate in that airspace you will have to be compliant with the rules they set. I also don't believe the CI will start their own FCL division as its currently done by the UK CAA on their behalf.
What it might mean is that they will adopt a lighter touch to maintenance and the associated regulatory fees. But the big incentive I see for people going onto the new reg is the more friendly tax schema.