I can just speak from my experience with PTSB, and that is they increased rates quiet quickly back in 2010/2011 - with their variable rate going to 6.15%. They came under some pressure because AIB at the time was something like 3.5% (can't remember exactly), and they where both more or less State owned.
So, their rates have come down to be more inline with the average variable rate, but that still does not make me trust them not to do something similar down the line.
I have no experience with AIB, so cannot comment on them.