They will continue to compete on costs.
There are only a very few true low cost carriers. Those limited low fares airlines such as easyJet and Fly.be will have to remain away from the low cost carriers or take them on by also becoming low cost.
I don't think there is any record of a biggish airline truly converting to low cost operations. Ryanair did it when it was a failure as a small traditional carrier. The only successful carriers in that mould have all started operations using the South West model in their own countries.
By the time Ryanair have expanded across Europe, N Africa and the Middle East nobody here will be in a position to care what happens next.
Just looking forward to lots of very affordable travel in the decade or two !!