It depends on when, how you define technology, and on how you define "advanced".

First, I'll restrict the definition of "technology" to innovations in physical devices and constructions, since advances in administrative technology are hard to qualify, or even define as "advances" linearly.

The first thing that should be noted is that the Byzantines, of the 12th century let's say, still knew about all the technologies present in the 2nd century Roman empire, but they tended to be more conservative in implementing them. Aqueducts, bathhouses, fountains, curiosities like automata, etc. were still built on occasion, but not at nearly the same scale as during the Pax Romana.

There are a few reasons for this:

A: the Byzantines maintained previously constructed Roman infrastructure in most cases, so there generally wasn't a need to build more (a major reason why most of the middle Byzantine aqueducts we know of supply new monasteries).

B: There was an urban and economic decline in the 7th century that made building expensive projects like aqueducts just to transfer water to a single place less rewarding.

C: Tastes had changed in regard to large public constructions. While in the Pax Romana huge bathhouses and public gathering places had been all the rage, so to speak, Middle Byzantines tended to prefer smaller, more private institutions, especially outside of the capital.

In the fields of technological advancement that we tend to associate with the Roman empire then, the Byzantine empire was at the same level, though they didn't implement that technology on the same scale as the Roman empire of the 2nd century had.

Now, for technological advancements between the 2nd and 12th centuries in the Roman empire. In the time between Marcus Aurelius and Manuel Komnenos, there had been no small amount of innovation. The Byzantines had many technologies that the classical Romans didn't, including:

1: Lamellar. Lamellar, steel plates sown together by leather, functioned as a cheap alternative to mail, and allowed the Byzantines to outfit more soldiers with steel armor than they could otherwise

2: Quilted armor. A very cheap, but effective, armor that, like Lamellar, further allowed the Byzantines to protect more soldiers, better. Quilted armor was also used to bard horses at a much lower cost than mail or leather.

3: The dromon. The dromon was a faster, more effective galley than those of the 2nd century. These dromons also tended to use lateen sails, which allowed boats to tack against to wind, unlike the square sails used by most classical Roman galleys.

4: The stirrup. Adopted by the Roman army in late antiquity, the stirrup allowed a rider to lean to the side on a saddle, and generally made riding more comfortable, which made training and fighting much easier. They also made it much harder to unseat a cavalryman, which contributed to the effectiveness of the next innovation,

5: The couched lance. While the effect of the couched lance is often somewhat overestimated, it functioned as a more effective and longer reaching alternative to the old Byzantine shock weapon, the mace. In the right circumstances, a couched lance was also one of the few weapons which could pierce chain mail outright.

6: The mace. Though not terribly complicated, the mace was a very effective blunt force weapon, something lacking in the marian arsenal, which could injure or even kill through helmets and mail.

7: The plumbata. The plumbata was a large lead-weighted throwing dart invented in the late Roman period. It replaced the pilum as the Roman infantryman's missile weapon of choice, doing a similar amount of damage while being much lighter and easier to carry. A Roman infantryman would have three or four strapped to the inside of his shield, and would throw one or two before engaging in melee.

8: The crossguard. Crossguards protected your hand from getting injured or cut off while fighting. While they were invented long before the Roman empire, they were gradually adopted by the Roman military from the 6th century onwards.

9: Greek fire. Probably the most well known of Byzantine inventions, Greek, called liquid, Roman, or median fire by the Byzantines, fire throwers were pumps used to spray a flaming oil-based mixture against enemies. By the 12th century these flamethrowers came in two forms: the large cylinder pump based variant, used on ships and occasionally mounted on a frame or wall on land, and the Handheld variant, used to disrupt enemy formations and burn ships or enemy siege engines when necessary. Greek fire famously saved the Byzantine empire from destruction when it was used to break the Arab naval blockade in the 718 siege of Constantinople.

10: The counterweight and traction trebuchet. The trebuchet in both of its variants were major improvements over the old Roman onager and ballista, and allowed fortresses and cities to be taken in a much shorter timeframe. The counterweight trebuchet may have been invented by Alexios Komnenos himself, who was known to have been mechanically inclined, though that isn't known for certain.

11: The pendentive arch. Pendentive arches were an architectural innovation which allowed a dome to be set upon a square base. A favorite of Byzantine architects, the most famous examples can be found in the Hagia Sophia supporting the massive central dome.

12: The squinch. While less elegant than pendentives, squinches also allowed domes to be set upon a square base, but required less space to accomplish this than a pendentive arch did, and so they feature heavily in smaller churches. Squinches were essentially octagons set upon a square base, which were close enough to a circle to mount a dome upon.

There were likely more inventions that I don't remember at the moment as well.

In conclusion, the Byzantine empire was more advanced in technological knowledge, but some technologies weren't implemented as universally as in the classical Roman empire. The main reason for this survival of technology in practice compared to western Europe was the full survival of the classical scholarly tradition in the Byzantine empire, and the empire's strong central government, which facilitated the maintenance and construction of large scale infrastructure.

Sources and further reading:

"The Age of the Dromon, The Byzantine Navy ca. 500-1200 ad" by John Pryor and Elizabeth M Jeffreys

"Sowing the Dragons Teeth, Byzantine warfare in the tenth century" by Eric McGeer, which contains within it the Praecepta Militaria of Nikephoros Phokas and the Taktika of Nikephoros Ouranos.

The aqueducts of the Sumela, Stavronikita, and Simonopetra monasteries, 12th to 13th centuries. The emperor Andronikos Komnenos is also described building an aqueduct in the History of Niketas Choniates.

The bath house of Thessalonica, late 12th to early 13th century.

The "Stratigikon" of Maurice, and the "Taktika" of Leo VI

"Byzantine Heavy Artillery: The Helepolis" by George T. Dennis