First of all, what do you mean by Byzantine? At no point did people living in the empire or the rulers call themselves Byzantine? What specific traditions and legacies were so significantly ruptured? I know some people like to set the date of the fall as 1204, but I have a hard tome accepting that fact and want to get your comprehend your understanding of the subject. It could be argued that more significant breaks happened during the reign of Heraclius (r. 610-641) and his Hellenization of the empire. While the 4th Crusade and the Latin Kingdom of Constantinople hastened the decline decline and fall of the Empire, I have a hard time accepting that the Palaiologoi represent a significant break,

Alright, now that I've fleshed out some of the ideas and I don't the pressure of plans that I've made, it's time to just answer this question.

Before getting into answering the question (sorry), I think it is necessary to consider modern perspective of change over time. The Roman Empire lasted for a fucking long time, and I think that that fact is incredibly difficult for modern people to comprehend. Even Europeans, who have the benefit of seeing relics of the medieval and classical past all around them, institutionally speaking, do not operate within a state system that has been operating continuously for more than 2-300 years (yes, Britain, I know you are a special snowflake, we can talk about that later). While the legal traditions of Europe are quite old, the constitutions of most Western countries are no more than 300 years old. With that in mind, we moderns tend to conceive of periods of significant rupture. With 500 more years of perspective (assuming the United States lasts that long), Jacksonian democracy may not be as big of a break as it does to us with little under 200 years of perspective.

Now, on to the question at hand. To answer this question I reviewed Ageliki Laiou’s (RIP ☹ ) contribution to the sixth volume of the New Cambridge Medieval History. Besides that, a lot of this information is coming from my experience working with the primary sources and historiography of Italians in the Aegean in the late fourteenth and early fifteenth centuries. Happily, Laiou is THE leading late Byzantinist of the last 50 years or so. If you can read French, this volume will have all the answers you’re looking for, http://www.worldcat.org/title/monde-byzantin/oclc/55122664&referer=brief_results. If you can’t read French, Constantinople and the Latins: the Foreign Policy of Andronicus II, again by Laiou (http://www.worldcat.org/title/constantinople-and-the-latins-the-foreign-policy-of-andronicus-ii-1282-1328/oclc/416484) is a great book and highly recommended.

With my original thoughts in mind, I think the pertinent question is not whether the period after the “restoration” of the Palaeologoi to the throne in Constantinople represents a significant break from the period before 1204, rather than the supposed unbroken chain that extended all the way back to the establishment of the principate under Augustus. Even within the first Imperial dynasty, the Julio-Claudians, the principate was a constantly evolving animal and the position was constantly changing throughout the Middle Ages.

Laiou helpfully breaks down the post-1261 (I’m using this date because it marks the signing of the Treaty of Nymphaeum) Roman Empire down a under of ways, but a couple are most relevant to the question at hand. Vaguehorizons citation of Bartusis is a bit hasty, I think. Bartusis is concerned with the Byzantine Army, a problematic topic during this period. That said, there SO many sources for this period of Byzantine history. That said, militarily speaking, we can make a few statements. The very small native Roman army, post-1261, was organized around the institution of the pronoia, that is land grants in return for service, an institution that extended back to the 11th century. The navy, on the other the other hand, was reduced drastically and Italians took over control of the Aegean and the Black Sea. This was done because of lack of funds.

There was also significant continuity in terms of the aristocracy. Even during the period of the Latin Kingdom of Constantinople, major outlying lands within the Empire remained in the hands of traditional Aristocratic families. While the power of the aristocracy, relative to that of the Emperor, increased post-restoration, the same network of aristocrats remained relatively constant since the 12th century.

Judicial structures represent the significant break. The creation of the Latin Patriarchate and the diffusion of judicial authority amongst members of the clergy during the Latin Kingdom of Jerusalem represents a rather significant change. Yes, more judicial authority was vested in the clergy during the hundreds of years leading up to 1204, I think the influence of Latin structures of power and the importance of the clergy to social structures in Western Europe caused significant changes within Roman society. Additionally, the Italian states introduced numerous extraterritorial zones, something that should not be underestimated and was really rather significant in terms of the big picture of the late thirteenth and early fourteenth century Roman Empire.

Finally, economically speaking, the period after the restoration represents a VERY significant break. This is something about which I feel rather comfortable talking about, but I’m not sure that it has a huge amount of relevance to the original question, which concerns institutions.

Question to the OP: if continuity is the issue, wouldn't you just start following the Empire of Trebizond? (The Comnenus/Komnenos state in exile until 1461)