Secessio plebis could be compared to XVIII century emancipation of middle class. It was a struggle between hereditary wealthy (aristocracy) vs acquired wealth of middle classses. Like American revolution and similiar emancipation in England and Europe.

Both sides were relativly wealthy people but birth rights were giving them unequal status.

So not really a conflict between rich and poor. But of course populist side claimed tactical class solidarity with city's poor people. Later on bipartisan system of optimates and populari stayed for years but the division lost its practical meaning.

https://www.britannica.com/topic/Optimates-and-Populares