Hard to answer.
As for their biggest competitor, I'd say: In Japan, definitely Nintendo. In Europe, I'd say PC. In North America, Xbox and Nintendo share that spot.
However, as for the biggest threat, I would say mobile gaming. And that's not just for Sony, but also for Xbox, PC and Nintendo.
Case of point: I gave my nephew my Switch and Super Mario Bros 3 to play. He didn't like it. I thought it was because of the outdated graphics, but he answered that it is too complicated. And yeah, he died 3 times against the same first Goomba, both in SMB3 and in SMB (which he did dislike because of the outdated graphics btw). I gave him the Dragon Quest Builders demo, but he couldn't figure out the controls and couldn't leave the first room as a result. Ironically maybe, he's very good at Snipperclips Plus instead. My wife, who never played Videogames outside of her Smartphone before, plays Super Mario Kart 8 Deluxe, but zigzags more than a sleepy drunkard. She's just unable to understand that the kart will drive forwards by itself without any input from the player (and no, she doesn't have a driver's license!)
They, and probably a whole Generation along with them, are more used to play things like Hungry Shark, Hay Day or some Match-3 clones. Things that don't need any effort or are just puzzles. Console or PC games need a minimum of effort an rarely are just puzzles, and thus seem to much already for them. Unless we can teach them how to play and what makes a good video game, I fear the market for consoles and PC gaming will shrink in the coming years.
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454