Whenever i look into Roman history i always notice that the first Roman Emperors(Like Claudius or Augustus) are often depicted wearing laurels, but when i look at pictures of Byzantine Emperors(Like Justinian or Constantine IX) they are most likely depicted wearing golden crowns. What is the reason behind this difference?
Edit: Warning, you'll quickly see why my flair says "Byzantine History" and not "Roman History" !
It's because the Byzantine Empire was in some ways Roman, but other ways not at all. This is one of the ways that they were not.
The Early Roman Empire was more like a faux-republic (Think Russia or Francoist Spain). The institutions of the Republic mostly remained intact, Consuls and Quaestors were still appointed and the Senate still sat in their house and argued, and this is the case until Leo the Wise institutes the Basilika in the 9th century and removes most of the remaining Roman institutions. Alongside this, for a multitude of reasons, the early emperors didn't want to be looked at as Monarchs, Augustus refused to let people call him rex, for example, preferring the term "Princeps" which means first citizen. This doesn't really change until the reign of Septimius Severus and doesn't really go away completely until Diocletian institutes the Dominate and begins to peel away the false republic in favor of the de-facto Empire.
So why the laurels?
The Laurel you are referring to is the Civic Crown, or the second highest honor a Roman citizen could achieve. It was given to men who saved fellow citizens and as such it was truly a high honor. Augustus wanted to use this as his symbol, supposedly because it symbolized that he saved millions of people by ending the Civil Wars, and later emperors kept this tradition going. It was the symbol they could have to show their authority while keeping the visage of a republic alive.
So why did the Byzantines stop this?
A variety of reasons, basically. For one, as I mentioned above, the fake republic continuously eroded until it was a mere sham. The Senate stopped doing anything really, the title of Consul became united with that of Emperor under Leo the Wise, Roman government titles were replaced with Greek ones, etc. With these institutional legacies dying off, there's less of an impetus to abide by the customs of a republic that was long dead. The Eastern people also were just generally much more accepting of monarchal rule than the Romans. An often understated aspect of Byzantine governance is how much eastern traditions were infused with Roman ones to make the "Byzantine" Empire. Political mutilations would have been looked as appalling under the classical Romans, while in Byzantium it was the expected punishment of basically anyone who opposed the government in some way if they weren't just straight up executed. Visitors of the Emperor were expected to fully prostrate themselves and kiss the ground, while prior the "First Citizen," would either expect nothing like this or accept a mere bow. These two factors together are what allowed the Emperors of Byzantium to fully announce themselves as "Emperors." Symbolically you see this with the fact that Heraclius stopped using the title of Caesar (which eventually became a high court title, not the Emperors title) or Augustus (although it's part of the name of a few more of his descendants, the first guy I can't find any evidence of being Augustus is Constantine IV, his great grandson), but instead using the title of "Basilius," which translates to "Sovereign" in Greek but is generally recognized as meaning "Emperor." Alongside all of this, however, was the removal of any disgust at the idea of wearing a crown. Justinian and Theodora both wear one in their famous mosaics in Ravenna, many of the Eastern Roman Emperors of antiquity (at least I think, I can't see clearly enough in the pictures if they're Laurels or Crowns, but Theodosius I and his son Arcadius both appear to be wearing crowns) wore crowns in depictions and in coins, and the Byzantines eventually actually got quite good at making them! The famous crown of St. Stephen (which is unfortunate in that it depicts the evil nitwit (light hearted sarcasm) Michael VII) is a Byzantine Crown and the potentially fraudulent Monamachos Crown (Which depicts sisters Zoe and Theodora, Daghters of Constantine VIII, Nieces of Basil II and the last legitimate Macedonians, and Zoe's husband Constnatine IX Monamachos).
So, for short, the Romans didn't wear them because they preferred to keep up the false Republic, while the Byzantines didn't care and quite enjoyed their gold.
As a follow up question, would the idea of a crown as a symbol for kingship even be familiar to early romans (or other people living during antiquity)? Is it truly such an old symbol?