I don't believe it does. Everyone is equal. At a past operation I worked at, we occasionally had problems with an unnamed jet operator, trying to tell us to 'hold out there until we land'. Needless to say, it went down like a lead fart, and more often than not we'd refuse to do so, and continue on our merry way. Always worked out that we'd create little, if any, disruption to their service.
Just because you're flying around in a 70 tonne metal tube, doesn't mean you have automatic right over 2.5 tonne metal tube,
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Airmanship can change it slightly though. But that's out of courtesy of the PIC, not because "they're bigger than us".
morno