In addition to what has been stated above, the majority of military histories on the subject are written from a very Anglocentric perspective, often depending on rather biased sources (such as Gerald of Wales, and other later commentators in the same tradition) that have a pretty clear rhetorical purpose in their description of the Irish as inferior to the English in matters of war. Even within that tradition, the English writers (or Anglo-Norman/Cambro-Norman if you really wish to be specific), there was a general trend that emphasized the difficulty of fighting the Irish in Ireland, and the different conditions that necessitated a different sort of warfare: Gerald of Wales, who is generally incredibly derogatory toward the Irish, notes that armor is more of a hindrance in Ireland than it is an aid, and that the key to victory would essentially involve using a lot lightly armed and armored cavalry (i.e. the Irish way of war) and lots of archers. In many ways, that is in and of itself a rhetorical statement meant to argue for the primacy of his relatives in Irish affairs--Gerald was a close relative of many of the first Norman mercenaries in Ireland, and many of them either died fighting the Irish or were displaced by later Norman nobles more amenable to the King--and he wished to emphasize that their unique skill set honed on the Welsh Marches was more appropriate to an Irish context than the more conventional "French" method of war involving heavy cavalry charges over relatively stable terrain.
It's also worth noting that the Irish enjoyed quite a bit of military success against the English, and many of the early English successes were probably not influenced overly much by military differences between the two nations, and more due to the political situation of the time: Irish regional kings, seeing the advantage to be gained by hiring English mercenaries and appealing to the English Crown (who was more French than English at this point), often collaborated with Anglo-Norman mercenaries, who took advantage of dynastic struggles to ingratiate themselves into the political landscape. Certain kingdoms of the Irish remained more or less unthreatened by English encroachment, or after some initial misfortune, soon regained their authority to the extent that they remained unconquerable until the Tudor era.
It's also worth remembering that the Irish military system was not really all that different from its contemporaries in other nations. Regional kings, later styled chiefs of their name, maintained a household of warriors on their own land. They in turn held the fealty of other, smaller chiefs with their own retinues. They would generally be equipped as mail-clad light horsemen, but for pitched battle would also frequently dismount and fight on foot in ranks. Mercenaries, both domestic and foreign, were common, and became more common over time. Essentially, lords retained professional warriors, and were given military service by lesser lords who in turn retained professional warriors of their own; as time went on, many nobles became itinerant mercenaries. Skirmishing tactics were common, but they were common in other regions of Europe as well: Spain, the Baltic, the Balkans, etc. So Ireland wasn't really that much of an outlier, but rather consistent with certain other trends in European history, Just not the Anglocentric ones typically privileged in the historiographical tradition.
One last thing to consider: almost all military battles in post-Norman invasion Ireland (calling it the Norman conquest is an outmoded misnomer, since they did not conquer Ireland by any stretch of the term) would involve Normans and Irishman on both sides of the battle. Nearly every Irish king went to war with some Norman allies at his side, and nearly every Norman noble went to war with Irish allies. These alliances were often tenuous, and it can be hard to tell who was the "senior partner" so to speak in many cases, but the lines between Gael and Gall were at once ironclad and extremely fluid. Ironclad in the sense that even if a Burke or a FitzGerald spoke Irish fluently, adopted Irish manners of dress and warfare and such, they still considered themselves English/Norman (and were considered as such by the Irish); but fluid in the sense that it was local and regional conditions that often dictated one's political allegiance in practical terms, even if in theoretical terms ultimate fealty was owed to the English Crown and its representatives in Dublin.
EDIT: I should cite sources. "Irish and Anglo-Norman Warfare in the Twelfth Century" by Marie Therese Flanagan and "Gaelic Warfare in the Middle Ages" by Katharine Simms, both from
A Military History of Ireland, ed. by Thomas Bartlett and Keith Jeffrey. Both good secondary resources. "Images of Warfare in Bardic Warfare" by Katharine Simms also provides some valuable information on how the Irish portrayed themselves in war.
For primary sources, I recommend
"The Triumphs of Turlough", and Viscount de Perellos account of his visit to the O Neill Mor
here.