Hey FEBF!
I specifically designed my Divine Abilities in Ascension to roughly equate to those in Deities & Demigods.
I think it really just boils down to Divine Ranks.
Official Demigod = DvR 1-5, my version DvR 6
Official Lesser God = DvR 6-10, my version DvR 8
Official Intermediate God DvR 11-15, my version DvR 12
Official Greater God DvR 16-20, my version DvR 16
My Demigod is tougher, their Greater God is likely tougher, but overall its likely not a big disparity. The only thing I would avoid in their rules is that individual divine ranks trump lower ones. So a DvR 9 Lesser God trumps a DvR 8 Lesser God. I would ignore that.