Yes Ravenna did change dramatically during those years, but not necessarily because of the switch between Ostrogothic and Byzantine rule.

I'd first like to note that the life of a lower class individual (such as a craftsman, slave, small landowner, merchant) would have not been particularly changed after all the disastrous events of the 530s, although their life definitely would have been affected by the events when they occurred. An upper class individual (Roman senators, Ostrogothic nobility, military leaders), on the other hand, would have been permanently effected by the catastrophes that impacted the social fabric of the Northern Adriatic during this period.

The main effect of the Gothic War on the Adriatic coast that Medievalists love to analyze, especially in recent years with Chris Wickham's neo-Marxist revision of Late Antique historiography and the interest in subsistence economics, is the depopulation that occurred in the mid-6th century. Ravenna was a ceremonial urban stage for the Byzantine and Ostrogothic aristocracy who profited from the work of the lower classes in the countryside, so an explanation of the decimation of the lower class in this region and the subsequent lack of funding for the patrician inhabitants of Ravenna is crucial to answering your question. This will help us define what exactly this 'change' was and why it occurred.

The Byzantine and Ostrogothic armies did plunder agrarian communities along the Adriatic, which undoubtedly would have impacted the importation of grain into Ravenna, effectively destabilizing the population of the maritime metropolis. This is often used by military historians as the explanation for the swift conquest of the former seat of the Byzantine Empire on the Italian Peninsula by an upstart Germanic nation, the Lombards. Much of Chris Wickham's scholarship discussed the apparent loose organization of the Lombardic Kingdom and its inability to salvage the urbanization and intellectual traditions of Roman Italy as the Ostrogoths had.

A better explanation of this sudden and dramatic fall in population would be the two natural disasters that appeared to have occurred in these exact decades. In the late 530s a volcano eruption spewed vast quantities of ash into the atmosphere, leading to widespread famines and initiating what may have been a spiritual crisis for those living in a major ecclesiastical center such as Ravenna. In the 540s outbreaks of the bubonic plague emanated out from the imperial capital at Constantinople, making its way to Ravenna via trade routes and frequent shipments of soldiers to the Byzantine army under the general Belisarius. The plague was so detrimental to the army's numbers (which declined from approximately a hundred thousand to, as Belisarius claims, five thousand) that Justinian was forced to recruit tens of thousands of frontier mercenaries to send to Italy as reinforcements.

The consequences of this depopulation in the countryside and the city and the migration of a giant foreign army through this region can be seen vividly in the abrupt decline in Ravenna's prestige. No Roman or Gothic writer emerged from these years as a successor to Boethius, Cassiodorus, or Symmachus in the literary and intellectual traditions that had been established at the court of Theodoric only decades earlier.

Similarly, the churches, baptistries, and royal buildings that were built in Ravenna in the first half of the 6th century were some of the last examples of Late Antique architecture on the Italian peninsula.

In Ravenna, the last large public building to be constructed was the Basilica of Sant'Apollinare in Classe, completed in 549. Like the other major churches (San Vitale, Sant'Apollinare Nuovo), the Arian and Orthodox Baptistries, and Theodoric's palace and mausoleum, it had been begun earlier in the century and was primarily funded by the great nobles who envisioned Ravenna as the new administrative capital of Italy. Without wealthy leaders such as Justinian or Theodoric to use and patronize these buildings as a means of manufacturing an imperial image of themselves with ceremonies, processions, and holding court, there was no need for new buildings.

It's hardly surprising that, instead of demolishing the Ostrogoths' attempt at creating a Roman city or erecting new churches, the triumphant Roman nobility and Byzantine army in Ravenna simply appropriated the buildings for their own use. In Sant'Apollinare Nuovo, Byzantine mosaicists placed the name of Justinian above a portrait of Theodoric and removed the figures of Theodoric and his court from a mosaic depicting Theodoric's palace (notice the disembodied hands still extant in the columns of the palace).

Were these small artistic revisions made because there were fewer Ostrogoths living in Ravenna (presumably due to years of war, famine, and plague)? Did Byzantine leaders no longer have to take into consideration the opposition of a large ethnic minority to the public display of Byzantine orthodoxy and supremacy? I would like to think so, although it's always difficult trying to pinpoint the specific historical context of a work of Medieval art.

The change that occurred is what Chris Wickham has termed a "fiscal breakdown". While the Ostrogothic royal court at Ravenna had managed to extract taxes from the local Roman landed aristocracy, the death of many of the laborers on these large plots of land during the 530s resulted in a failure to continue accruing funds for any local expenditures like monuments, schools, defensive structures, or military campaigns.

To answer your question by using a modern analogy: imagine that you are an individual living in Detroit for the past fifty years. Formerly a major industrial engine at the heart of the American midwest, the city's importance as a political and economic center as well as an arbiter of culture has decayed and crumbled to the point that it is a hollowed out skeleton of its former glory. The ghosts of its past tower over its horizon, so to speak.

Hope this helps! Please reply with any follow up questions!

(sidenote: the sources I'm recalling were the linked articles on 6th century natural disasters, my exhaustive knowledge of Late Antique art, Procopius' The Gothic War, Boethius' Consolation of Philosophy, Cassiodorus' Variae, Chris Wickham's essays on Lombardic land economics and his book The Inheritance of Rome, and various overviews of the appropriation of Roman art in Theodoric's royal court in Ravenna)