Does the Fire Phoenix seem like the no-brainer choice? Obviously if you don't fight, discard this comment.
But once a week (which is a reasonable spend of catalysts and relics), you can power through the last 2 rounds of the tournament with a huge buff.
Its also the best on pop/sq, and its final bonus is IMO the best (though the KP from Storm is probably equal). Fire is weak in mid-stages (coin rains - bleh), but even those rewards aren't bad. And if we're talking min-maxing here, I'm mostly focused on Level 9-10. Maybe that's the wrong approach until its clear how many levels we can pick up if we 100% the event, though.
But just thinking out loud:
-Storm Phoenix's food effect is only good if you have MM spells up (which for me is somewhat rare). Maybe if you make it your strategy to always have an MM running on a T3 factory? But then you're spending Catalysts/relics to craft food, and you're either also crafting MM spells (so you'd better have a level 5 MA, and never craft anything besides food), or you're using your MM spells from tourneys (and now have one less source of spell fragments). Either way, it seems like you have to go "all-in" to really maximize Storm.
-Storm also has IMO the worst collection items for end-game. Mana and broken runes? Meh. Mana is nice, but if its a 48hr collection, that's hard to time to be really effective.
-Aureate Phoenix's food effect is really nice, but how often are you going to be running pet food? Again, it seems like you have to convert your MA into a pet food factory, and prioritize pet food spells over everything else to get the full effect. Otherwise its like having a Level 25 MH (without the pop) for 1-2 collection(s) a week or so. This is based on my read that the spell lasts for 2 hours (i.e., 1 collection). Assuming a 3-3-3-9 production cycle, and you only do it on the 9s, that reduces the value down to something closer to a level 8 MH. Which is nice. But a level 8 MH isn't particularly hard to come by, and again, opportunity cost.
-All of this depends on the availability of pet food spells. The event looks like it gives a nice stockpile, but I'm not counting on that stockpile lasting forever. So if 2-3 spells a week is easy to keep up, maybe it shifts the balance. But being able to time Fire's benefits with tournaments means you only need 1 a week to feel like your building is really contributing to your city. Whereas the other two, I'd feel like I need to run pet food at least once a day to really get the full benefits.
-Its a shame that all of these buildings are wasting "building points" on providing coins.
-Obviously a lot of this analysis depends on the final math.
-The analysis also assumes future events will provide set buildings like prior events. Like a level 10 Aureate Phoenix, on a per square basis, is a real tier goods production powerhouse, on a relatively tiny footprint. But if I'm realistic about future events, I'm probably able to find "high goods productivity" in future sets, whereas I'm not sure I can necessarily get "free military buffs plus never-ending portal profits." There was a nice run of having consistent temporary military buildings in AW recipes, but AW recipe bloat is getting real, very fast. With the chess set, and some pet food recipes, and who knows what else in the future, temp military buildings are feeling very scarce.
Anyways, just rambling. All input would be appreciate.