I know it's not the question you asked, but the most important thing is that you and your girlfriend do an agreement on the purchase of the house. You will find a very old draft here, but it outlines some of the principles
http://www.askaboutmoney.com/showthread.php?t=5003
if I put her name on the BOI mortgage application, we don't get the Mortgage we need.
Are you saying that if you apply on your own, Bank of Ireland will give you €100,000, but if you apply jointly, they will give you only €90,000? This would be astonishing if it's true.
If you have most of the deposit and most of the income, you are probably better off buying the house on your own. If your girlfriend has a good contribution to the deposit and a good contribution to the repayments, a joint purchase is fine, as long as you have an agreement in place.
If, by any chance, your girfriend is in financial difficulty, e.g. a lot of creditors or unpaid bills, you should not buy jointly.
ptsb or Bank of Ireland?
There is really no way of knowing. Bank of Ireland is robustly pushing to maximise profits and avoid having to raise additional capital. ptsb is still state owned and is not under the same pressure. ptsb is well aware of the very negative impact on its reputation of the SVR issue last year. They will be slower to risk this again.
But, in reality, there is no way of knowing.