IMHO, The Conduit, Call of Duty WAW, and Medal of Honor: Heroes 2 all are great games with great online. There are things each does better than the others, however I think all 3 are great games. The meh graphics in MOH can easily be overlooked by the amazing gameplay and 32 player online (and current $20 price tag). COD looks great, plays great, with lots of weapons, but not many modes of online play, and only 8 players. Conduit is graphically rough, but the most fast paced and very "GoldenEye, Doom, Quake-esque.
I've spent time with them all, and as stated above, I like the gameplay online in MOH, the fast paced feel of the Conduit, and the visuals of COD, but here are some more details. I will omit non online games here, as that seems to be one of the things the OP is interested in.
Conduit:
Pro's: Best variety of online play, 13 in all with 7 maps and 18 weapons. ASE football is crazy fun, Bounty Hunter is very unique, Three Strikes is fun, Marathon (DM), Team Reaper (TDM), Team Objective (CTF) and more. Online multiplayer supports 12 players. Uses Wii Speak. Great gun graphics. Crazy customization options. Extremely fast paced and crazy online play, very fun.
Con's: Short mediocre (though not poor) story, though it does get very hard late in the game especiaaly at high difficulty. Infrequent issue that can leave a player "lost in space" for the round. Background textures and envioronment repetitivity can get tedious.
Call of Duty World at War :
Pro's: Best FPS graphics of the online offerings on the Wii. Good single player game, fun multiplayer. Great variety of weapons including flamethrower. Online not laggy, looks great. This is very fun also.
Con's: Though several online options, all are really Deathmatch or Team Deathmatch. Less options than the HD versions (vehicles, CTF, Zombies). Only 8 players online. No Wii Speak.
Medal of Honor : Heroes 2 :
Pro's : 32 players online, with six maps. You can play many ways, fast run-n-gun, hide & snipe. Deathmatch, Team Deathmatch, Infiltration (Capture the Flag), Online leaderboards.
Very creative gun use, twist the Wii remote to Zoom on a sniper rifle, while hiding, lean by "leaning the nunchuck" (works great), Bazooka is help with the Wii Remote backwards on your shoulder (works great). Lots of nooks and crannies to hide in, creative angles to snipe from. Amazingly fun. Not only is the single player campaign a pretty good one, it also has an "Arcade mode" which is a first person on-rail version of the single player campaign. So this is really 3 games in one, and all 3 are extremely good!
Con's: Lame graphics, the same as the PSP. Textures are reaslly not bad, the character models and animations are the problem. However in this game graphics are definitely not as important as the absolute great gameplay.
MOH:H2 is really and unfairly overlooked, the gameplay, price, amount of players really make this game extremely worthwhile.
Overall, I think all 3 are very good games, if you prefer your FPS with IR instead of thumbing joysticks, all 3 are well worth your investment.