On the other hand, consoles are the leaders, and the PC is the follower, when it comes to lots of other genres. 

Platformers and Party games, indeed.

Edited to make more sense.

Not really, no. There hasn't been a single revolutionizing shooter, strategy, rpg, adventure, etc. on consoles. They jsut end up copying half-life or diablo 2, or other well known games. Yes consoles have things like Mario 64 and Guitar Hero, but as noted, those are the party and palforming games I mentioned earlier.

Edit: 1 more genre, Fighting. Much better on the consoles than on PCs.

So right now the score is:

Consoles: Platformers, party games, fighting

PC: FPS, RTS

On the chopping block --
MMORPG (I'd say PC just because that's where the action seems to be)
Sports (I vote console, reasoning similar to MMO)
SHMUP (I vote console)
JRPG (I vote no advantage -- consoles get more action but I dunno if there's any inherent superiority of consoles)
WRPG (I vote no advantage -- see above, only PC)
SRPG (I vote no advantage -- see above, consoles again)
Point-and-click adventure (I'm inclined to vote PC, reasoning similar to MMO)

hahahaNO.

shooter -- Assuming you mean FPS, console still had Goldeneye which was crazy multiplayer action and didn't it innovate in its 'missions' if not elsewhere?  (I remember that game pretty well but I'm far from expert on the PC stuff so I can't compare too well.)

strategy -- If you mean RTS, I'm sure you're right -- unless Pikmin counts. 

rpg -- Seriously?  Seriously? 

adventure -- I hope you don't mean "adventure" as in "Zelda". 

How do you communicate in MMOs? Surely not voice chat. Also what action seems to be there? FFXI is the only decent MMORPG on a console and even that is very limited compared to the PC one. Theres a reason people buy it for the PC not the PS2.

I'll give you SHMUP, for the simple fact of the old school shmups on the good ol' systems.

JRPGS are basically TBS games with a more linear story, something the PC dominates at. Far easir to manage Civ4, total war, etc. with a mouse than a JRPG. Hate scrolling through menus and targets.

WRPG- Look at NeverWinter Nights, Baldur's gate, etc. You can't pull that shit off on a console. NWN had 36 hotkeys FFS (ctrl and shift modifier keys to all the F keys).

SRPG- Look at my reasoning behind JRPGs, except you get Fire Emblem which is absolutely badass.

Poit and click - Agreed, hard to point and click with analog sticks.

Shooters, before GoldenEye there was Quake several years earlier. Though the missoin things weren't as cool, multiplayer was much easier to handle mostly because of controls.

Adventure- I hope you don't mean that Zelda innovatted as much as King's quest, 2 years before Zelda. The closest thing to adventure is Zack and Wiki, which sadly didn't sell so well. Should have sold a lot more it was hella fun.

And yes, RPGs. Hack and slash games have been ripping off Diablo and JRPGs have been ripping off older dungeon crawlers from the PC.

Quite nice list, however I would change wizardry to ultima.

Wizardry: Proving Grounds of the Mad Overlord / 1981

Ultima I: The First Age of Darkness / 1980

Ultima had back then free roam world(!!) plus dungeons that were like wizardry. (And it came out earlier. :P)

PC was the heavy innovator in the early days, as this video clearly shows.  In the mid 90s, Console gaming overtook it in both popularity and productivity.  And many of the 'innovation' that made the PC so great started to be seen on the consoles.  There's a reason many people claim companies like Sierra and Blizzard 'revitalized' PC gaming in the late 90s...because they partially did.  At least pumped much needed interest and revenue into the PC gaming industry.

Anyway, I saw this back like 3 weeks ago or whenever it first showed up.  And I think its one of the better ones they did.  Many genres (and companies) started from these games.

MMOs - You realize that the consoles now support keyboards?  And that I agreed about voting PC for MMO, and that I'd already said the reason you cited?

JRPGs - If you're saying Civ4 is the same type of game as a JRPG, I think we have a fundamental disagreement far more serious than whether PC or consoles do it better. 

SRPG - this makes even less sense to apply that same argument to. 

Point and click - Zack & Wiki uses analog sticks now?  But I agree on the vote. 

FPS - so you're saying PC pioneered MP and consoles pioneered SP? -- I can live with that.  

Other:
May I remind you that in this part of the discussion you are in the position of defending "There hasn't been a single revolutionizing..."  Did Zelda not revolutionize the genre?  AT ANY POINT EVER?  Ocarina of Time?  Love it or hate it, did FF7 not revolutionize JRPGs? 

Right now the score seems to be

Consoles: 
-Platformers
-Party games
--(including music/rhythm games apparently)
-Fighting games
-SHMUPs
-Sports games

PC:
-FPS
-RTS
-TBS
-WRPG
-MMORPG
-Point-and-click adventure

In contention: 
-Zelda-type adventure (honestly the NAME ALONE...)
-JRPG (consoles IMO)
-SRPG (ditto)

On the chopping block
-Racing sims
-Arcade racers (shall we include kart racers in this, or is it a separate one that Nintendo wins by default?)