3 missionaries for most faiths means that you hold Rome directly. It takes time before that's a realistic consideration. Even with a juiced Hindu with "enforced heritage", "movement support", "monastic education" and "save the burning world plus religious (giving base 2 + 2 +1 +3 = 8% strength from decisions) I couldn't keep up with even garden variety mid-late game expansion on 2 missionaries with Hindu. Keeping in mind that I had religious, so my actual base strength was 13%, that's crazy.
But if I were Coptic, I could have kept up in conversions easily, because rather than 2 missionaries, I'd have 5 (Mecca, Jerusalem, DotF), plus the other benefits DotF confers (with no risk of CtA in their case). Sure, the Christian decisions I'd take would only give me 2-4% strength (depending how much I care about not tolerating heretics), but that's 7-9% strength on 5 missionaries. It completely trashes the conversion rate of even 3 missionaries at 13% strength. A 9% strength missionary can convert a hostile culture Sunni province with 20 development and not take that long. Heck with an inquisitor and +1 stab that converts Mecca, and that's before cathedrals. Everything else gets swiftly converted in sub-20 months.
Even at 13% strength, most provinces take 8 months to convert (11 for Sunni). 2 missionaries converting provinces in 15 months (20 for Sunni) will win, but even Coptic is often faster than that.
It's no contest really, and the lack of DotF is painful because of how handy that is for a little morale and a lot of -WE.