You will see many authors still clinging to the concept of a "Byzantine University", a fact illustrated by the very title Wikipedia uses.
A most prominent example would be Paul Lemerle's "Le premier humanisme byzantin: notes et remarques sur enseignement et culture à Byzance des Origines au Xe Siècle". An otherwise enlightening text about the structure and foundations of the higher education and its development in Constantinople. (Chapter "The first three centuries") But it seriously wants to paint an 'origin story' for the European universities of the Middle Ages, emphasising more the similarities than the differences.
And one of the most important differences was highlighted by Paul Speck's 1974 study "Die Kaiserliche Universität von Konstantinopel: Präzisierungen zur Frage des höheren Schulwesens in Byzanz im 9. und 10. Jahrhundert" – still using the disputed concept in its title again! The problem is indeed rooted in the very name of the concept questioned here: Corporate structure.
In medieval universities we see privileges conferred to – one – body of scholars, professors and students, providing 'universal' education (that is many subjects) with not only certain rights – but also autonomy on how to run things internally and towards external entities. This is analogous to guilds and corporations!
While in Constantinople we see a lot of traditions transmitted from antiquity: a lot of schools, only loosely bound together by a bureaucratic bond that is much more personal in nature than legally institutionalised, from the top down to the students: emperor to bureaucrat, emperor to teacher, teacher to student. A conglomerate of different schools instead of one institution, subdivided by faculties.
This is what the line from Wikipedia really means:
At the time various economic schools, colleges, polytechnics, libraries and fine-arts academies
also operated in the city of Constantinople.(correction mine, debatable whether using brackets would be more appropriate?)
… and what is reflected in various tidbits throughout the article.
In Byzantium, after the Pandidakterion came to be, public and private schooling were to be kept apart, but by no means was private tuition banned. Just a teacher had to decide whether to do one or the other. The medieval monopoly for (local) higher education was absent. Being a public lecturer at the Pandidakterion had certain advantages, and tuition fees were sometimes levied, sometimes not, but private teaching could grant just the same level of recognised education.
A variety of institutions transmitted official knowledge for official, state purposes. A practical matter, although founded on the classical tradition, but comparatively very little research as l'art pour l'art.
A Latin school gave out degrees in Latin, a Greek grammarian likewise for his field, but a museion and a library would operate independently, as did schools for oratory or legal texts. But an individual school was mostly dominated by its teacher, wielding much more power than things like 'tenure' would confer.
In summary, the lack of a campus, the lack of uniting legal structure and institution, and the lack of autonomy would be the main differences to observe. Curiously, the results of closing Plato's Academy and other places of learning (like Antioch or Alexandria 'lost' to Muslim expansion), meant that Constantinople in effect became one giant campus, being the place of higher learning in the empire, with a lot of schools and chairs operating there.
The lack of autonomy may be exemplified by the following passage:
Everything points to the sixth century marking a pause and then a decline in the great burst of enthusiasm which sprang from the foundation of Constantinople and the renewal of the Empire. This enthusiasm had swept Byzantine civilisation along for two centuries and allowed it to incorporate again, more or less securely, the thread of ancient civilisation. It is certainly not that research and higher education, the Library and the School and with them the artes liberales, disappeared. […]
Yet the Church must not be blamed: the State which Constantine had founded had chosen to identify itself, in a sense, with the Church and religion, and, in this sense, Justinian's measures were logical.
Cod. Just. I, 5, 18, § 4 decrees that those who do not follow "the catholic and apostolic Church and the orthodox faith", the heretics, the Jews and the pagans, can neither serve nor be honoured with any rank whatsoever, nor "under cover of any form of teaching whatsoever, draw simple souls into their error".
Cod. Just. I, 11, 10 made this brutally clear:
"We forbid any teaching to be carried out by those who are infected with the sacrilegious foolishness of the Hellenes".
It is in the context of the measures taken against paganism that we must interpret what is called the closing of the School of Athens.
More on the differences especially in
Judith Herrin: "The Byzantine "University" - A Misnomer" (Ch2, p17–28), in: Kjell Blückert, Guyneave & Thorsten Nybom (eds): "The European Research University. An Historical Parenthesis", Issues in Higher Education, Palgrave Macmillan: Basingstoke, 2006.
The institutional differences concerning a largely personal tie in imperial protection and funding are also highlighted in the appearance and dis-appearance of the Pandidakterion. We do not see a 'Byzantine University' in operation from the founding of Pandidakterium in 425 to 1453. Nor do we see a convincing case for labelling the School of the Palace Hall of Magnaura a direct continuation for it. This 'line of tradition' seems instead heaviily fractured into many phases:
It is almost certain that the Pandidakterion did not continue after the reign of Herakleios (610–641); more correctly, perhaps, we have no evidence that it did.
After that, the state will undertake no further action in the field of ‘higher’ education and, apart from the constitutio Omnem, it will be more than two hundred years before the next state initiative: the establishment of the school of Magnaura (855), […]
After Leo’s death (post 869) all traces of Magnaura are lost and there is no evidence to show that the school continued to operate for any length of time.
The last attempt at creating a higher education institution in Byzantium came, as is widely known, from Constantine IX Monomachos (1042–1055) with his very important novel of April 1047; with this text, drafted by John Mauropous, the preexisting (private) school of Michael Psellos and John Xiphilinos, which had two “orientations”, philosophy and law, was divided into separate schools—a school of philosophy under Psellos and a school of law under Xiphilinos. Yet, despite the ample information we have about the establishment and regulations of these institutions,a s well as about their early years, it is almost certain that they did not continue for long; indeed, the law school does not seem to survive beyond the year 1054.
— Athanasios Markopoulos: "In search for ’Higher education’ in Byzantium", Zbornik radova Vizantoloskog instituta, 2013.