Piggybacking off of what u/malcomiiicanmore has said, it is also important to recognize that authority in Scotland wasn't fully and entirely centralized until the end of the sixteenth century.

Throughout the medieval period, although the Scottish crown held ostensible authority over the affairs of government, there were examples of powerful magnates who flouted that authority and pretty much did as they pleased. Indeed, sometimes these magnates were the king's own children, as is the case of Alexander, earl of Buchan, the "Wolf of Badenoch", who burned down Elgin Cathedral because he got into a tiff with the Bishop of Moray.[1] Moreover, Gaelic Scotland was still quasi-ruled by the Lordship of the Isles until James IV broke the MacDonalds in 1493; that is, the MacDonald Lords of the Isles had been known to make independent treaties with magnates and with various kings of England in defiance of the crown, and as Gaelic Scotland still operated, at that point, largely along the lines of kinship and alliance,[2] many clans allied themselves to the MacDonalds and had little interaction with the Scottish court.

I cannot speak to the political structure of medieval and early modern Ireland as I don't know enough about it to comment; however, if you are interested in reading more on Scotland, I would suggest the following titles:

Boardman, Stephen I. The Early Stewart Kings: Robert II and Robert III, 1371-1406. East Linton: Tuckwell Press, 1996.

Brown, Keith M. Bloodfeud in Scotland, 1573-1625: Violence, Justice, and Politics in an Early Modern Society. Edinburgh: John Donald, 1986.

Lee, Maurice. Government by Pen: Scotland Under James VI and I. Urbana: University of Illinois Press, 1980.

McDonald, Russell Andrew. The Kingdom of the Isles: Scotland's Western Seaboard, c. 1100-c. 1336. No. 4. East Lothian, Scotland: Tuckwell Press, 1997.

Macdougall, Norman. James IV. Edinburgh: John Donald, 1989.

References:

[1] A. Grant, "The Wolf of Badenoch" in Moray, Province and People, ed. W.D.H. Sellar (Edinburgh: Scottish Society for Northern Studies, 1993), 151, 152.

[2] Alison Cathcart, Kinship and Clientage: Highland Clanship 1451-1609, (Leiden: Brill, 2006), 59-129; 159-209

Although I specialize in Scotland between the central and later middle ages, my research centers on the portrayals of Malcolm III and, in part, Macbeth, in Scottish historiography from the aforementioned centuries. As a disclaimer, therefore, I admit I am not the aptest historian to explain broader similarities between Ireland and Scotland. However, I would like to clarify aspects of the premise on which your question rests. Eleventh-century Scotland did not equate to the territory that comprises modern-day Scotland. We do not have much surviving contemporary evidence produced by Scots from the eleventh century so our understanding of the period rests primarily on Irish and Anglo-Saxon sources; the sources that do survive from eleventh-century Scotland have made it to us via later medieval manuscripts and have a rather complex transmission history (see Professor Dauvit Broun's work on John of Fordun's Chronica Gentis Scotorum, The Irish Identity of the Kingdom of the Scots). At the time, the kingdom of the Scots comprised around one-third of what is modern-day Scotland; Orkney was a Norwegian earldom while there has been much debate on the status of Strathclyde, Moray, and Lothian in the eleventh century. Scotland as a 'nation', the way we understand modern nationhood, did not exist at this time. Local politics, regional and linguistic differences, and cultural diversity were probably more characteristic of the kingdom of Scots at the time than often assumed. We should not assume so readily that Ireland and Scotland, therefore, were very similar kingdoms.

To illustrate this point, Alex Woolf has argued in From Pictland to Alba we cannot assert that Scotland was the 'only Celtic realm with well formed and independent political institutions' in the eleventh century. As Woolf has further argued, 'Scotland was, eventually, to outstrip Ireland in the race to statehood but, in the mid-eleventh century, this was a race which had barely begun." (p. 350).

To understand the complexity of the kingdom of Scots in the eleventh century, I recommend the following books:

Alex Woolf, From Pictland to Alba, 789-1070. The New Edinburgh History of Scotland, vol. 2. (Edinburgh: Edinburgh UP, 2007). G.W.S. Barrow, Kingdom and Unity, 1000-1306. 2nd ed. Edinburgh Classic Editions (Edinburgh, Edinburgh UP, 2015) A.A.M. Duncan, The Kingship of the Scots, 842-1292: Succession and Independence (Edinburgh, Edinburgh UP, 2002).