LOL House...
But House wouldn't WANT the artifact unless it was something like The Golden Vicodin of Ghengis Khan (KKKHAAAAAAAAAANNNNNNNN!!!!!!!!)
Batman might want the artifact to keep it AWAY from the Riddler or Joker...
Indy wants it because he's Indy...
Holmes was contacted a couple times by the royalty to find things for them, so maybe...
And Bond would be ordered by M to get it before some villian.
So, my take:
The first thing Bond EVER does while on a mission is... do whatever is NOT the mission. Pussy Galore indeed...
So he's WAY behind.
Indy takes off like a bullet, hopping from place to place...
Batman would take a bit of time to research in the Batcave, then off in the Jet or Batmobile, pretty fast...
Holmes might be the best at spotting nuances of the four, but he also has the worst transportation- horse buggy, a train or steamer if he's lucky.
After a little screwing around, Bond decides to get down to it (take that as you will.) He usually has GPS something, so he's probably tracking the others, and sees that Indy's the closest, and takes off in his new car in that direction.
But he gets intercepted by thugs and captured... because 007 always needs to get captured at least once.
He uses his gadgets to escape, but he still loses time.
Batman and Indy, too, have to fight off bad guys.
HOLMES, meanwhile, has been relatively enemy-free, with the exception of the occasional thug, and that's nothing he can't handle. He's now cracked the crucial part of the code (whatever it is, always a code for these treasures) and takes the lead.
Indy escapes the Nazis and is close behind, and Batman's on his tail.
Bond's been captured again... turns out once again his squeeze was a hired gun...
Holmes arrives first, but needs help. Indy obliges, as Holmes doesn't want the trophy anyway, just the satisfaction of cracking the case and notoriety and pay that comes with it, so Idny afterwards can still have the artifact for his museum.
And then along comes Batman.
Holmes and Indy don't play by the rules quite often.
Batman doesn't HAVE rules... except two- don't kill, and WIN.
Holmes' cane and revolver are no match for knockout gas... he's out.
Indy's whip proves more dangerous... until a Batarang slices it in half. Indy's still got his gun- another Batarang. He's still a great fistfighter... he and Batman are equally matched there... but Batman's still darker and has more gadgets anyway... Indy's out.
And, just as Batman's loading the artifact onto his jet... fresh from three captures, four fire fights, one supervillian, and five hours of sex on the autopilot plane...
The name's Bond- James Bond.
They gadget fight for a while... but their toys are equally matched. They fight for a while, but Bat,an's in for more than he bargained for- this isn't the joking Moore Bond or the "troubled" Craig Bond, or the dull Lazenby/Dalton Bonds... not even the suave, sophisticated and awesome Brosnan Bond.
This is THE Bond... the alcholic one... the CONNERY one.
So Connery Bond's plenty able to keep up with Batman fist to fist... they're equally matched... but then-
Help.
Who's Bond got on the bench? Pussy Galore, THE Bond girl, sexy, dangerous, and with the most incredibly porno-inspired name ever for a Bodn girl.
And Batman has... Robin. Nightwing. Batgirl? Who cares- NONE of them can beat a Bond girl!
So while Robin plays boy scouts and faster than you can say "Holly Raging Hormones, Batman!" he gets his little ass handed to him.
And Bond has the artifact and... yes- Pussy Galore (he snuck Natalya and Jinx on the plane, too... Brosnan Bond wasn't happy...)
;)