Sony under pressure with PS3 produced some good games, but it was never as good as the PS1 or PS2, when they were dominant. PS4 was more consistent in quality.
Nintendo did a lot of its best work when it was riding high. For the NES, they initially had the pressure of convincing people to buy a video game system after they felt burned by Atari, Intellivision, Colecovision, etc, but a lot of their best work came in the later years of the NES, when they were so dominant they could hold Wal-Mart to ransom. The Genesis did put some pressure on the SNES in the West (and the SNES came about in part because the PC-Engine was starting to pressure the NES in Japan), which led to things like DKC, Nintendo rolling back its Hays Code policies for Mortal Kombat, and their subsequent arcade partnership with Midway. The PS1 seemed mostly to put pressure on the Zelda team to make Ocarina of Time as amazing as possible to regain their honor after Final Fantasy VII jumped ship to the PS1. The Gamecube was actually more enjoyable than the N64, but SMS and MKDD didn't hit quite as hard as SM64 and MK64 did, though WW and TP were phenomenal. That said, the pressure to perform against the PS4 and XB1 did give rise to the Switch, and the Switch 2 is almost a perfect system to me, just because of the breadth of the library and the increased performance over the S1.
In some ways they didn't even seem to be trying with the Wii U, yet a lot of the Wii U's library ended up getting ported to Switch, which was good.
Nintendo's games are solid to phenomenal, but the main way in which "pressure" manifested with them was in their willingness to work with third parties, something which Sony took for granted. Pressure to ensure a steady stream of third party releases on N64's successor and move away from their "kids' image led to a port of RE2 on N64, which led in turn to the Capcom Five. They mended fences with Namco in the last years of the N64, and Namco helped them fill the RPG and fighting niche somewhat on Gamecube with SoulCalibur 2 (with Link), Tales of Symphonia, and Baten Kaitos. For the Switch 2, they're now getting a lot of big third party games day-and-date from companies like Capcom, Square Enix, and CD Projekt (which released TW3 Remastered day-and-date on S2).
With Xbox, Microsoft's solution to all their problems was to keep throwing money at ithem. The 360 succeeded more because of unforced errors on Sony's part than because of anything Microsoft was doing. Apparently now the parent company is no longer willing to throw money at Xbox without some kind of return.
