History

first off, the welsh were treated pretty much as badly, the history of wales since the norman conquest has been one of fairly brutal colonisation and repression. the reason it's not perceived to be as bad is because wales was essentially fully assimilated and integrated by the modern period and the memory of that is more distant. there's also the fact that since it was a largely medieval affair rather than early modern, the methods of suppression of the welsh identity were less totalistic than those applied in ireland (though there are similarities, for example the way welsh language was repressed wholesale during the victorian period).

regarding the irish, there's a more religious dimension to consider as the irish stuck with catholicism much more than the inhabitants of britain did on the whole. this was troublesome for the british crown as the protestant churches of britain were a key mechanism of state power over the populace. thus to subjugate ireland it was necessary to enforce british religion on ireland. with the way that religious identity can be tied up with cultural identity, it hence became necessary to try and replace the independent irish culture with a british culture - english or scottish, both played a role in the process of colonisation that followed (scottish colonisation of ulster was equally as important as english and it's not accurate to say that it was an english project alone).

plantations were the main way in which the british crown tried to accomplish its goals. there were four major waves of plantation from the time of Henry VIII through to James I (who was a scottish king, highlighting the point made at the end of the last paragraph). what were the crown's goals exactly? the mercantilist ideology of the state sought profit for english and scottish landlords in ireland. how best to achieve this? seizing land from native irish landholders (whose form of ownership was more traditional and localised), and handing it out to english and scottish ones (whose concept of ownership was early modern capitalist in form). here we see the core reason for suppression of the irish - the traditional structure of irish society had to be demolished in order to enforce the new, more extractive british system. this is in contrast to earlier norman domination of ireland which had been a feudal affair and did not challenge irish society to nearly the same extent.

i would write about the reasons scotland didn't face colonisation or suppression in the same way but @jack already handled that pretty well.