What football team is better, Northern Ireland or the Republic of Irelands?
I would say Northern Ireland and I will give a scientific reason.
They have one of the smallest populations from which to draw from when selecting a squad and this is further complicated by the fact that Northern Irish players can opt to go to the Republic of Ireland squad. The Republic of Ireland squad pays more too and so a lot do.
Despite this the Northern Irish squad have performed well. They are pretty much a good bogey side. They play mediocre against teams that are considered on a par but when playing against a good side they often pull it out of the bag and win.
Football in Northern Ireland is vastly underfunded when you compare it to other parts of the world or even UK. Despite this they quite often qualify for major competitions (even sometimes when Rep of Ireland does not).
So what drives them if it's not money etc. Northern Irish people when faced with the thought of evaluation from the outside world will literally drive themselves to the point of exhaustian. They will give everything they have just to raise people's evaluation. This is because Northern Ireland for years was looked on negatively because of the troubles here. (Territorial fighting between Republicans who want United Ireland and Loyalists who want to remain part of the UK)
The Northern Irish team will always enter any competition with fight in their bellies and a point to prove.
It must be said this is non-argument, like something from Gulliver's Travels, except for the teams involved. On paper the Republic is probably better but I would suggest there is a lack of belief in the present ROI setup, from fan to player, which in turn is having a knock on effect on everyone interested in the game in the Republic and beyond. (See Declan Rice's recent withdrawal from the ROI squad and Harry Arter's bustup with Roy Keane). This kind of acrimony doesn't exist in Northern Ireland, who have by far the better coach, and with fewer resources could have qualified for WC 2018 if not for an outrageous refereeing decision. The recent 3–0 win over Israel is a true reflection of where NI stands; the Republic's 1–4 loss to Wales is a reflection of where Martin O'Neill and Roy Keane are at.
The historical head-to-head record has 4 wins for the Republic, 2 wins for Northern Ireland and 4 draws.
Given the relative populations that's probably a fairly accurate indication of the likely win/loss probabilities in future games.
If the two were to play each other tomorrow (Thursday 27th September 2018) I would suggest form would make Northern Ireland slight favourites at a neutral venue - but that the match would likely go with home advantage.