Hmm. That IS a noodle-scratcher there, Bijoux.

So I'm allowed to pick just any incarnation of Sherlock Holmes to pit against the Scooby-Doo and the Mystery Gang?
Well gosh. My initial instinct is to immediately say that Sherlock will always trump. But then again... This charming fellow: doesn't believe that the earth revolves around the sun... I would imagine that most of the people in the Mystery Gang are at least aware of that little factoid.
I’m inclined to say that Sherlock would be at a disadvantage when confronted with supernatural beings, but considering that all of the monsters from Scooby-Doo are disgruntled real estate agents or custodians or something along those line, I don’t think it would be fair to give them home field advantage in the area of monsters. _{That would definitely belong to the Winchesters, but Supernatural isn’t part of this discussion...}

If I had to guess, the Sherlock Holmes from that link you have given me would behave more consistently with the collective notions of the character; most people (prior to the sudden revival he’s been enjoying what with the the Robert Downey Jr version, BBC, and Elementary) would likely say that Sherlock is a calm, sophisticated man with methodical approaches to his investigations, which I cannot help but feel might put him at some sort of disadvantage. But if I get to pick which version of Sherlock to go with and I choose one of the more recent versions, that disadvantage disappears...

Additionally, what sort of case are the two challengers investigating? Are we going with as possibility of the paranormal? Or a more traditional Sherlock Holmes case? What is the expected outcome of said investigation, a disgruntled janitor or something more like what would appear on Supernatural? Because if it’s the latter I would have to say that there is the chance that the Mystery Gang would get that one figured out conclusively sooner (though as I said earlier, I hesitate to give them the advantage in monster related fields), whereas I would easily give any variety of Sherlock the win when dealing with paranormal imitations pulled off by displeased employees -- such as is sort of the concept of the first Robert Downey Jr. Sherlock film.
If we were to turn around and give the Mystery Gang a case that would be more typical of a Holmes situation -- not counting Moriarty cases, because those ones are a beast all their own -- I don’t think they would figure things out nearly as quickly as he would.

I think I’m going to have to go ahead and maintain my initial thought that Sherlock would win. At least I will until you give me more details to make me reconsider my opinion.

I feel like this is a really convoluted reply. I’m sorry.

My god! You're right! What devilry is this?
...

Now you've got me thinking seriously though, can we really be sure that they are ahead of the other nations? Water tribe definitely, but we saw evidence of plumbing in the air temples.
Those Air Nomads could have had flushing toilets before they were wiped out. They could have been a whole century ahead of everyone else!

And they didn't think to share that technology...

I daresay that that is a distinct possibility there, Bijoux.

Although, I'm not sure I remember this decision of us determining that Yello's "Oh Yeah" is my most favourite song ever. Do remind me of when we figured this out. ;D

Thanks so much for finding me these, Corad! I really appreciate it.

What I glanced at on those non-dA sites really did look promising. I noticed that one of them forbid me from reading ahead, so I figured I'd wait until I had the time to follow the instructions to read through that one.

I'd seen a couple of the dA ones before. Actually, I think I'd favourited one or two of them before you linked me to them. Must be some sort of sign.

I feel like I'm going to have a hard time turning the left side of my brain off for this...