Both:

Wanted to be more legitimate than not; they wanted legitimacy, backed up by muscle.

Both towards the end of their lives viewed themselves as mainly businessmen, albeit viewing themselves as businessmen in a bloody business

Looked down on the street guys as not having a wide enough vision, but nonetheless took their money

Employed their own killers and profited from drugs and prostitution despite wanting to be legitimate

Both were seen to have inherited their leadership through nepotism - Neil Dellacroce and Joe N. Gallo were passed over in favor of Paul. Tessio and Clemenza were passed over in favor of Michael. (Note, Paul was elected to the position of Boss in November 1976, but still, some felt Neil was passed over).

Both were not seen as Street guys. Both committed a major criminal act but otherwise had a clean record. Paul was arrested for robbery in 1934 and served a year for refusing to talk about Applachin in 1960. Michael’s major criminal act inducting him as a made men was killing Sol and McClusky, but he had otherwise a clean record.

Both had civilian careers before their Mob life - Paul worked for his father as a butcher. Michael served in the Marines.

Both served as Acting Boss of their Families for a period of tutoring before becoming Boss. Paul was named Acting Boss in charge of the Gambino’s day to day actions in 1967, with an increasingly sickly and reclusive Carlo still having the final day. Michael became Street/Acting Boss for Vito upon his return home from Sicily and represented the family in day to day affairs, with an increasingly sickly and slowed down Vito still running things in the shadows.

Both were far removed from the streets. In GFII, Michael is said to be reclusive, up in Tahoe drinking cocktails. The implication is clear; he’s not a street guy, he doesn’t understand what’s going on in the streets. Street level guys like Pentangelli chafe under his remoteness and resent having to take orders from a remote almost feudal lord. Late in life, Michael claimed to be basically retired, yet still chaired the Commission and actively blocked Zasa’s rise in the Corleone Family.

Similarly toward the end of his life, Castellano was removed from the streets, in his mansion in Staten Island, only admitting high ranking Capos and his administration men, which made men in his family feel cut off from their Boss.

Both had a disdain for the street level guys but nonetheless took their moneyZ

Both did their best to heavily insulate themselves from lower ranking members but were almost undone by street level guys - Willie Cicci testifying against Michael, the lower ranking guys in the car theft case testifying against Paul

Both were introspective and shockingly wise men for their trades

Both admired more lawyers, soldiers, civilian warriors if you will. Recall Paul’s comment about cops being brave. Recall Michael wanting more lawyers around him and less gangsters

Both were sickly and diabetic toward the end and ruled toward the end of their life by women - Paul by his mistress, Michael by Connie. Both were cared for by these women which allowed them a large and traditionally unacceptable degree of influence.

Both took on the mantle of Boss as a promise made to a sickly relative. Paul said he was “called upon” to make a “promise to a dying man” in his words. Michael on what he thought was his fathers death bed pledged himself to his way of life

Both underestimated an up and coming gangster who was known for dressing fancy and being charismatic, both Paul and Michael viewing said gangster as little more than muscle, an enforcer. A debt collector. In Michael’s case it almost got him killed but for sheer luck; in Paul’s case it led to his death