The key to the Michael/Tom relationship is that Michael was an obsessive controller. He didn't need a consigliere because only his decisions counted, only his choices mattered. Tom was Vito's choice for consigliere, not Michael's. Tom was Sonny's choice for brother, not Michael's.
What's more, Tom wasn't a wartime consigliere. He says so himself, in the novel. He blames himself for Sonny's death--"old Genco would have smelled a rat." Michael may have resented Tom for that, fairly or not.