This guy is right on PS2, wrong on Sekiro. Here Ash: Godhand, Siren (1 and it's JP-only sequel), Shadow of Rome (eternal gem), Maximo: Ghosts to Glory (eternal gem), Maximo: Army of Zin (eternal gem), Urban Reign (eternal gem), .hack (both series), Dawn of Mana, Rogue Galaxy, Mortal Kombat: Shaolin Monks, Jet Li: Rise to Honor (better than PS1's Jackie Chan Stuntmaster although Jackie movies > Jet Li IRL even though it's close), Hungry Ghosts, Genji: Dawn of the Samurai, Matrix: Path of Neo, Shadow of Destiny, Pitfall: The Lost Expedition (severely underrated 3D platformer action adventure), Indiana Jones and the Emperor's Tomb, Ape Escape 2, Ape Escape 3, Ponie's Poin, The Adventures of Cookie & Cream, Shinobi, Nightshade, Dual Hearts, Crimson Sea 2, Justice League Heroes, Champions of Norrath: Realms of EverQuest, Champions of Norrath: Return to Arms, Eternal Ring, Legacy of Kain: Defiance, Soul Reaver 2, Tak and the Power of Juju, Tak 2, Tak 3, Jak and Daxter, Jak 2, Jak 3, Ratchet and Clank, Ratchet and Clank: Going Commando, Ratchet and Clank: Up Your Arsenal, Ratchet: Deadlocked, Sly Cooper and the Thievius Raccoonus, Sly 2: Band of Thieves, Sly 3: Honor Among Thieves, Kya: Dark Lineage, Radiata Stories, Crash Twinsanity, Shining Force NEO, Shining Force EXA, Spartan: Total Warrior, Silent Hill 1, 2, and 3 (maybe 4), Devil Summoner: Raidou Kuzunoha vs. the Soulless Army, Devil Summoner 2: Raidou Kuzunoha vs. King Abaddon, Soul Nomad & The World Eaters, Summoner 1 and 2, Code of the Samurai, Tenchu: Wrath of Heaven, Blood Omen 2: The Legacy of Kain, Baldur's Gate Dark Alliance I and II, Batman: Vengeance, Buffy the Vampire Slayer: Chaos Bleeds, Hulk: Ultimate Destruction, Okami, Viewtiful Joe 1 and 2, Evergrace, Bersek: Millennium Falcon, Forever Kingdom, Sword of Etheria, Way of the Samurai 1 and 2, Onimusha 1, 2, 3, and Dawn of Dreams, Blood Will Tell (true gem), Destroy All Humans 1 and 2.
PS2 completely mogs PSX.