My take, I don't think there was competition, suspicion if any

What did Don Vito Corleone see in Rocco Lampone
Originally Posted by Danito
Extract: So, just as Neri is Michael's Luca, Rocco is Michael's Clemenza

The only scenes, from memory -
  • Tom and Neri
The hooker murder / Geary compromise

  • Tom and Rocco
The new Don Tom asserting his authority! Dead Tahoe assassins
Quote
Tom: Alright, get rid of the bodies
Rocco: Where's Mike?
Tom: sternly, Rocco! [Then Tom walks off]
Rocco wasn't happy! taking orders from Tom

  • Neri and Rocco
The Desert Inn - when Michael said to Neri and Rocco to step outside, what I found really interesting was neither Neri nor Rocco engaged in any conversation whilst waiting to get back in. It was like they both avoided and kept their distance from each other!