I don't think City have been "blown out of the water" by anyone, though it has been argued by the press. The latest case is "Bruno" where the press linked us with him repeatedly despite assurances that City had no interest in the player whatsoever. There have been players we have shown some interest in, but ended our interest in, not because United blew little City away, but because the selling club wanted far more than City thought they were worth. Examples of this are Fred and Maguire. Oh and that South American fella who wanted the budget of a sovereign state a week in wages ... Then there are those like Pogba. City had been interested apparently but only the previous window and had ended their interest at the same time as Real Madrid, for two reasons in our case - Pepd had got his real target and Juventus wanted far more than we thought he was worth. When City buy a player it's a result of research, preparation and a deep assessment of value for money. In the past years our only serious rivals for players we really are interested in have been Real and Barca, and that seems likely to have changed.
It's a question of semantics but I see where you're coming from. Personally I think Pogba would have proven value for money at what United paid for him but he's the only example that comes to mind where I have a twinge of 'if only'. Maguire, Fred and Sanchez were bullets dodged.