I have to disagree with you on that for a few points. Sulla's party is composed mostly of the optimates who were the rich aristocratics. Those people tend to band together when the poor or common men rise up. Or when something threatens their position and power. Cinna right now is killing them and stealing there property. The optimates have a real threat against thier lives and money.Both are lead by very charismatic and ruthless men, who are the main glue of a loose union of highly ambitious, ruthless and arrogant Roman noblemen. And Sulla's party only lasted longer because he died after his main enemies, so he was able to try to solidify his system and allies in the institutions, which promptly fell apart when people (read the Triumvirate) tested it. So yes, if the leader die, the union goes into infighting unless situation is dire enough. It will be a question of time until either Crassus/Pompey/Sertorious/Cinna/Marius the Younger/someone is able to assert himself as the new leader though.
The Marian's on the other hand are made up of more opportunistic in nature being new men. They were fracturing before Marius had his heart attack and recovered. Now we have Cinna in Rome murdering his enemies both political and anyone he persevered as one in the past weather they are optimates or not.