Either it has bearing or it doesn't. One could easily argue a non-specialized RN is lesser educated when it comes to airway management or resuscitation. To automatically assume an RN is the "higher license" is hypocritical and smacks of the same type of provider bashing you accuse other of. You don't see Rad Techs, RRTs and RN's arguing over who's "higher" do you?
If you are working in a hospital, your job title and job description will spell this out.
If the EMT or Paramedic title is not recognized in the hospital and you are working under a different title, then you fall into the hierarchy for that title regardless of what you do on the ambulance.
Yes in the hospital there is a hierarchy between professionals depending on the circumstances and area. Each will also have their own job description and title. A Radiology Technologist with a Masters degree can oversee the Rad procedure but the patient will still be under the care of the RN who can also determine if a procedure should be stopped for the safety of the patient and for reasons which are out of the RTs area of expertise.
There are also many allied professionals who are required to have an Associates degree but are not on the same level as RNs, RRT or RTs.
PTA, OTA and some levels of Rad Technologists exist fall in a different level. There used to be a lower level in Respiratory also but I think they have gone by the wayside now or at least in this hospital. But, even for them they have different job description levels such as I, II or III similar to RNs which their level of expertise and sometimes leadership roles must be observed. All are also floated by their level of expertise and job description level. You would not put an RN I who has not ICU or ED experience in either area.
Would you put an EMT or even a Paramedic who has only done routine IFT transports on a 911 truck to do lead or be senior? I have known IFT Paramedics working on ALS transport trucks who have not started an IV or intubated in 5 years after joining that agency. They still are Paramedics. I think for Paramedics this might have a bigger influence since there is an expectation that all can do certain skills. Assuming that just because it is in your scope of practice for the state does not necessary mean you can do it either.
RNs, or most, do understand that regardless if it is in their state scope, they may not always be able to do it in their job description and those who have seen what other RNs do in specific areas like the many ICUs, they must have additional training and education.