Well, on the R/T EIN is "Shamrock" while EIR is "Eirjet", so that is quite a distinction. Otherwise surely there should not be any greater issue than there already is vis-a-vis airlines with similar three-letter codes, e.g. BAG/BAW, BMA/BMI, EZS/EZY, to name but a few?
If the actual numbers conflict - not an unusual occurrence in Irish airspace, with Ryanair and Aer Lingus already having several similar sequences of flight numbers - then it would seem preferable to use alpha-numeric versions of some for ATC purposes.