I'm not an expert or particularly qualified to answer but I'll try briefly tackling this. This is both a very simple and pretty difficult question to address. On the one hand, the key difference was the fact that the Republic was largely ruled by two consuls (elected for 1 year terms by Roman citizens, although the voting process tended to give more power to aristocrats) and the Senate (unelected aristocrats who were supposed to "advise" the consuls, but wielded significant power on their own), while the empire was ruled by, you guessed it, the emperor, with the Senate and Consuls as little more than figureheads. However, both time periods describe ~500 years of history (and, if you take the Eastern Roman Empire into account, which you should, that time frame extends all the way into the 1400s AD), time during which the republic/empire were constantly changing and evolving. Boiling this huge span of time into easy categories would be a significant undertaking I am not prepared to go into here. That said, I suggest going through some of the previous topics already discussed here that, although not directly responding to your question might give you some context, such as this or this or this. Additionally, the reasons for the fall of the Empire remains a hotly contested topic amongst historians to date (a ridiculous number of reasons have been given to date), so you should be careful about boiling it down to a quote.