Hope this helps...
Athenians and Romans are two words encompassing different times, spaces and political objectives. The word "citizenship" means different things for either at different times.
As for the word "better", needless to say one would have to state, fore and foremost: for whom.
Athens is an intelligence powerhouse between the VI and the IV Century BC. It virtually disappears after that under the heel of the Macedonians and the Romans.
Rome is a logistic and engineering forge between the VIII Century BC and the IV Century AD.
Their statutes were obviously very different as different were their needs and political objectives .
As for the "better system" you can rest assured that in both cases, whatever institutions they chose, they were best for themselves.
The very notion of "citizenship" was local in Athens (in Pericles time). If you lived in the city, had sufficient means and showed up in the Agora you could vote. There never were in Athens the hundreds of thousands inhabitants that peopled Rome at the highest of the Empire (II century AD).
Athens never had an Empire. Even the one allegedly created by Alexander never was one in the sense we give to the word today. Greeks colonies were independent political units often at odds with the mother country. There were no political links between them, as there were no links between the kingdoms conquered by Alexander. An Athenian was an Athenian if he lived in Athens.
A Roman citizen could live in Rumania and claim "Civis Romanus Sum". Paul did when he was captured on his way to Damascus.
Yet, this did not mean that he could vote for the Roman Senate. He couldn't even if he lived in Rome. In fact the Empire had done away with any formal popular vote that could never be implemented.
In conclusion, the answer to your question is: let's not make cronological errors. Citizenship means to us a combination of allegiance and rights. This combination might have existed in Athens and Rome (it did), but it was not guaranteed by an institution, allegiances were different over different territories and rights could change, in both places, with time and with the whims of the ruler
