I don't know what it is, but I get the feeling that Wizards of the Coast are worried about Paizo and Pathfinder, but Paizo isn't worried about Wizards of the Coast. I've never really gotten the impression that Paizo is trying to pull customers away from D&D over to Pathfinder. It's like the company is so comfortable in their own skin that they just continue forward without a care in the world what Wizards does.
Now I could be wrong entirely, but that is the impression I am under.
Paizo almost went under shortly after they started due to the realities of the magazine publishing buisness.
Then they almost went under after they lost
Star Wars Insiders.
Then they were worried about going under when they lost
Dragon and
Dungeon.
Then they were worried about going under when launched a line of 3.5e accessories the same time WotC announced 4e.
Then they were worried about going under when they doubled down on 3.5e and launched the Pathfinder RPG.
Now they're the leader of the pack. They have a solid and devoted fanbase. They have the largest current Organized Play program that might rival the best of the RPGA.
Even if WotC decimates their sales, they still have enough clout to keep going with their Card Game, novel line, and Adventure Paths. The APs are also potentially system neutral, so if D&D Next shatters all records they can just segue into supporting that edition, even if it's just providing conversion notes.
5e could hit Paizo hard. Really hard. The company has been growing at a steady pace buoyed by heavy sales. If WotC starts taking back sales that might lead to belt tightening at Paizo as they have to trim staff they can no longer support. But I don't think they're in danger of going under any more.