The new tactics are certainly a boon, but I think the main advantages lay in the political structures of the Despotate.
Unlike Frederick's part of Sicily, Alexandros is pretty much undisputed ruler in his land, no vassal to beg to or to convince following the military decisions you took.
The more concentrated political structure of the Despotate enables a more coherent and lasting strategic vision, which is a net plus in a war against Frederick's barons.
Besides, as Alexandros alluded to in his defiance of Frederick before the parliament, and Theodoros has shown off Amorgos in his dealing with the Hospitalers, the Greeks have a more pragmatic, flexible approach, which contrasts with the more ideological position of Frederick; that means in practice Frederick might get some early wins, but in the long run, Alexandros is just going to wait him out.
That might be something like: the royal army plus mercenaries invade, Philantropenos refuses open battle and wage guerrila, while Vatatzes galleys sink the royal fleet, raid royal and enemy barons domains from the sea, until Frederick who is stuck in multiple sieges, sees his treasury bleed, his forces whittle down from desertion and mercenaries who could not longer be paid, attempt to raise taxes, some barons finally think the war against Alexandros is not worth the new taxes, peasants have enough of the same taxes... Unless Frederick is lucid enough and can overcome the humiliation and not fight to the end even if alone, the war is going to end with Alexandros at the gates of Palermo and deposing Frederick.
He could then seize the crown for himself, as he has a valid claim, but that would mean extending the war several more years to reduce other barons, like Ioannis did in the Peloponnese, but with his own domains in eastern Sicily ravaged by the invasion and western Sicily being far less amicable to the perspective of a Greek ruler than in the east, I doubt he would be keen to indulge unnecessary blood spilt. It would be far easier for him to put Frederick's infant son Peter (born in 1304 if I get it right) on the throne and Queen Eleanor, Robert's and Ioannis' (in-law) sister, as a more friendly, reasonable and pliable regent.