I found the same information in the literature. But the confusion is, in some literature, they take the onset value at the peak beginning, and in some are taking onset value of the peak ending or take peak maxima. So which one is correct?
I would recommend for example if you have a phosphorescence spectra at 77 K to take the onset on the high energy side. The onset is a very good estimate of the 0-0 transition which is the energy difference you're after (the largest). taking the peak centre might be 0-1 or 0-2 transition which does not properly represent the full T1 to S0 energy gap. The intensity of the 0-0 transition is weak/absent because of the Franck-Condon principle.
Experimentally I would also recommend collecting with a sufficient time delay to ensure you're not collecting any emission from a singlet state.