Totally depends on the genres. I think Western companies and Japanese companies excel at different genres.
FPS – Western companies own this one. Western companies have made groundbreaking and influential FPS games such as Doom, Quake, Duke Nukem 3D, Goldeneye 007, Battlefield, Far Cry, Crysis,
Perfect Dark, Halo, Call of Duty, Fortnite, Overwatch, Unreal Tournament, Half-Life 1/2, Bioshock, Borderlands, Deus Ex etc It’s not really even close.
Sports – again, Western companies. NBA 2K, FIFA, NHL, MLB etc EA, Activision and Take Two (all Western) own a significant slice of the sports genre.
Adventure / Open World – This I’d have to give to Western companies too. Zelda and Yakuza notwithstanding, the vast majority of great adventure and open world games are from Western companies. GTA, Red Dead Redemption, Watch Dogs, Assassins Creed, Tomb Raider, Horizon Zero Dawn, Uncharted, Last of Us etc
Action / Hack and Slash – This is an interesting one. There’s both great Japanese games here like Devil May Cry, Dynasty Warriors and Bayonetta and Western ones like God of War. I’d say the advantage still goes to Japanese here though for overall volume of making these types of games. A lot of anime types like Hyperdimension Neptunia, Senran Kagura, Fire Emblem Warriors etc would go into this category as well.
Simulation – Western companies as well. I don’t think Japan even has many games in this genre. Sims, Civilization, Anno, Tropico, Cities Skylines, Sim City etc all Western
Racing – This is another interesting one because both Western and Japanese companies make great racing games. Western companies make Burnout, Forza, Need for Speed, Test Drive, Midnight Club, Wipe Out while Japanese companies make Mario Kart, Sega Rally, Ridge Racer, Gran Turismo, F-Zero. I think it’s totally a wash here as both Japan and Western companies make great racing games.
Fighting – Easily Japan. Japanese companies popularized the genre with Street Fighter II and further made progress with games like Virtua Fighter, Soul Calibur, Tekken, Dead or Alive, Guilty Gear, Blazblue, King of Fighters etc it’s no doubt that fighting games are one of Japanese companies’ strong points. Also beat em ups like Double Dragon, Battletoads, Final Fight, Golden Axe and Streets of Rage would also go here as well
Strategy – We have to make division between strategy and tactics. For tactical video games, I would have to give it to Japan for games like Final Fantasy Tactics, Fire Emblem, Advance Wars, Tactics Ogre, Disgaea etc and for both turn based and real time strategy its easily Western companies with games like Warcraft, Starcraft, Dune, Total Annihilation, Command & Conquer, Red Alert, Age of Empires, Civilization, Tropico, Empire Earth etc Western companies basically own the strategy genre.
Horror – I think although Alone in the Dark was a pioneer in this genre, this has to go to Japan with two of the most influential series in this genre – the Silent Hill and Resident Evil series. Although I like Dead Space and System Shock 2 too.
Platformer – clearly Japan. Japan took Activison’s Pitfall and raised the bar to another level with Super Mario Bros. Super Mario, Contra, Mega Man, Castlevania, Sonic, Metroid, Donkey Kong Country etc all took the platformer to another level.
RPG – This is the most interesting category because JRPGs and Western RPGs are so different. JRPGs have made their mark with games like Final Fantasy 6, Chrono Trigger, Earthbound, Secret of Mana, Terranigma, Super Mario RPG, Phantasy Star 4, Shining Force II, Dragon Quest 11, Persona 5, Chrono Cross, Suikoden II, Panzer Dragoon Saga, Lunar Story, Skies of Arcadia, Kingdom Hearts, Xenogears etc standing as some of the greatest RPGs ever.
On the other hand you have groundbreaking Western RPGs like Diablo 2, Witcher 3, Fable 2, Elder Scrolls: Oblivion, Mass Effect 2, Dragon Age Origins, Baldur’s Gate 2, Ultima IV, Wizardry 7, Might and Magic 6, Knights of the Old Republic, Fallout New Vegas, Planescape Torment, Neverwinter Nights, Dark Sun etc that are also equally good, but different. I mean how can you compare a game like Oblivion with a game like Chrono Trigger? It’s not comparable, they are totally different games but both RPGs and great in their own ways. So I have to call this category a total wash.