Being a citizen came with various perks. Somewhat relevant to your example, in the 60s AD when Christians were cracked down on in Rome, St. Peter was crucified, St. Paul suffered a much quicker execution in the form of beheading, as a Roman citizen could not be crucified (SPQR 521). Roman citizens in the Empire also had the right to appeal to senior officials, such as the prefect of Egypt, procurator of Judea, proconsul of Syria, or equivalent. Even these local methods of appeal were stymied by huge administrative backlogs: for instance, in the 3rd century AD one Egyptian prefect received in three days 1800 petitions from citizens wanting to press cases or complaints. As Beard puts it, "the majority...must have been brushed under the carpet" (464). People would generally turn to religion, the supernatural (465) or plain old rough justice to get even with somebody who had wronged them (463), but Roman citizens could at least attempt some administrative or legal recourse to this.

The Emperor was a different thing from the regular administrative apparatus, powerful as that was in the provinces. He was a semi-divine figure, and for instance a runaway slave could claim asylum by clinging to a statue of the emperor, just as with a god (431). Starting with Augustus, the emperor possessed the legal power of tribunicia potestas, the old power of the tribune of the people to which Republican Roman citizens could appeal against the rulings of magistrates (365). Letters from the emperor to any particular community were proudly displayed in public via a monument (335).

Citizens could indeed make appeals to the Emperor. However, it took a lot of time, contacts and cash to get a complaint this far (464). The Emperor would also sit in judgement over certain legal cases that could not be resolved locally. In this task he was assisted by a bureaucracy that grew around him centered on the person of the ad epistulis, the Emperor's secretary, literally "in charge of letters". As this bureaucracy expanded and later took on military roles, the office of ad epistulis was split into one for Greek and one for Latin correspondence, with the latter being the usual language for military and official correspondence. From the time of Marcus Aurelius, military experts tended to be appointed to the role of ad epistulis Latinis , while intellectuals, sophists or rhetors continued to serve as ad epistulus Graecis (Exploratio 140). It was these latter men would that deal with correspondence regarding formal complaints and requests for legal judgement.

Despite this bureaucracy and powerful men such as the ad epistulis to filter what got through to him, the Emperor spent large amounts of time at his desk sorting through his administrative workload (SPQR 410). An example Beard gives is of Augustus being required to pass judgemnet on a brawl in Cnidos in Asia Minor, where a thug was killed by a falling chamber pot 'accidentally' dropped by a slave that the 'victim' was attacking: Augustus had to decide whether the slave or the thug was guilty.*

The Emperor would have had a team of slaves and freedmen who sorted through his mail, advised the emperor on recommended actions, and probably drafted most of his decisions and replies (410). Indeed, most letters from the emperor recieved by provincial communities and displayed on monuments would have been written by somebody else and perhaps given the literal nod by the Emperor and stamped with his seal (410-1).

• Though we unfortunately don't know what he decided, but probably the latter based on known Roman legal theory (SPQR 464)

Sources:

Mary Beard, SPQR, 2015.

Austin and Rankov, Exploratio, 1995.

I have a question as well. Several times when Paul was being beaten or horribly mistreated, he'd pull the "I'm a Roman citizen" card which seemed to be quite effective in getting people to back-off very quickly. Can someone summarize the perks of being a Roman citizen in those times? If it's been answered before, can someone post a link please?