There would be minimal difference between them. Both messed up in the fluffy times, both are now owned by us. Both continue to be loss making.
Without our input they would be bust.{we have put 20 Billion into AIB}
From your view that does not matter. You get your Mortgage and provided you keep to its terms you are grand.
Since both are trying to return to profit, ,there is little doubt that they will increase rates at every opportunity.
Ask yourself ,Can you can afford the Mortgage should rates go up 2%.
Also be cautious when they offer you any add ons, eg life cover etc, It maybe they have changed , but both Banks in the fluffy times did not give customers anything like the customers best options.