Melodi - Not sure why Dr wants to surpress longer or if too late to take ET test.
Long protocol because of suppression stage, allows all the follicles to grow and mature at the same time. it also takes longer period as additional suppression jabs before the stimulation jabs. On long protocol, I think you start the suppression on Week 3 after AF arrives.
Antagonist (short) protocol doesn't suppress so the follicle growth is not so even, and because no suppression, needs more regular visits to the doctor for monitoring (to avoid over/under stimulation). Also supposed to be more patient friendly since shorter period (and I guess the jabs not as painful as the suppression jabs?) Doc visits not so much issue in SGP but apparently in some european countries, they don't see the doctor for 1 whole week.
For normal aged women, supposed to be not much difference between number and quality of eggs between the 2 protocols, just a more even maturity of eggs. I think in some hormonal circumstances, they also will do long protocol to ensure properly suppressed before stimming.
Hope this helps.