Furthermore, how did the rest of the world view them? Were they seen as usurpers or legitimate rulers? I would assume this depends on who is doing the viewing.
Could you clarify what you mean by Latin Emperors versus Orthodox Emperors? If you are talking about eastern Roman (later Byzantine) and western Roman emperors, or are you talking about the Holy Roman Empire? The Holy Roman Empire was seen by the Byzantines as a complete sham. To the Byzantines (who saw themselves as the real Romans and Charlemagne as a Germanic chieftain who was getting a little ahead of himself. Typically, prior to Charlemagne, every western ruler still ruled by (in name only) permission of the Byzantine Empire. Even when Romulus Augustulus was retired in the west, the imperial regalia was returned to the east. Additionally, every symbol of power and even the coronation rites in most monarchies were borrowed from the Byzantines. Ultimately, this comes down to yet another east-west deal. The westerners saw Charlemagne as more legitimate because the pope had proclaimed him emperor. In the east, the pope was not seen as the successor of Peter and as having all the power he had (which caused the great schism), so this would not have carried as much weight. Charlemagne must have had enough detractors, however, because he was forced to justify his claim to the purple by saying that there was no legitimate emperor, only an empress (whom he subsequently proposed to). She had none of it, however. They did not view the holy Roman Empire as an empire. Charlemagne was only king of the Franks.