No positive difference at all. The troubles werent caused by the governments of either country, it was entirely the blame of the lunatic fringes on both sides that would not accept the situation as it was and decided to use terrorism to get try and get what they wanted.
There might (and its a big might) have been better co-operation from the ROI government regarding chasing IRA members hiding south of the border, but just the ROI being involved in the fighting wouldnt change attitudes towards Northern Ireland at all.
It could potentially make the situation worse, or make it all start earlier. There could be trained and experienced soldiers who come back from the war and decided that now was a good time to try to take back NI. Or at least start to get everything organised and ready, training others, acquiring weapons, that sort of thing.
Nothing either government did would have prevented the troubles from happening, even had the British decided to walk away from NI (something they couldnt do) would provoke trouble from the lunatics that didnt want to be joined with the ROI.