I feel I can answer this, as I believe I have a fair solution to all this, as well as tremendous power.
I hope you'll find my solution to this fair. Also unbiased, seeing as I am argueing for the allowance of Showdown despite my preference for PO.
For those users who can get both Showdown and PO, you'll try to agree on which one to use in regards to tournaments. If you can't decide, have another user flip a coin and whoever calls it gets to choose the platform. If for the Pokemon League, the preference of the Leader takes precedence over the preference of the challenger, meaning if I was challenging Spoink, who can use both PO and Showdown, he would have to use PO because that is my preference for battling.
Okay, easy there right, don't even think I needed to say that above part. Now here's where I can get some complaints.
We should allow both PO and Showdown in tournaments, so that we do not exclude users. If a person with just Showdown is matched vs a person with just PO, we'll swap the users around to fix that problem easily.
Now for the League. If Gym Leaders can use Showdown and PO, please do if the challenger has only one of those available to them. The league is made partly for the enjoyment of the users, and the other part is to give them a challenge. All of it is for the users. Who are we to deny users of this?
If a Gym Leader cannot use PO or Showdown and the challenger can't use the one that the Gym Leader has access to, there are two choices you should take. The first is to give a default badge, as is the case of blob. The second and more preferable choice is to have a part-time leader take over for that battle. Ninja, for you this is incredibly easy, as my brother is willing to use Showdown to battle people. He can just take on both parts of the 7th Gym.
For Elite 4 members though, things are different. We can't just take on part-time E4, as that greatly reduces the challenge of the Elite 4. Elite 4 members do take precedence. So if you only have access to PO and are at Speed Freak, you best hope that Mew ends up beating Speed Freak for his spot, because you aren't going anywhere.
As for those of you who have access to both while your challenger has access to one, just suck it up and do that battle with them. Making a Showdown account takes all of two minutes at the most. As for team-making, you get the import feature, and if it doesn't work you still have your PO team right there in front of you, so you can just manually put in anything missing. Takes all of five minutes there. Seven minutes of your life and you got to make this site more enjoyable for other people. Fair trade.
So yes, I say allow both PO and Showdown, but with these parameters. And considering the powers I wield, this is how it is going to be unless Pokemaster chooses to overide my descision for some reason, or if it turns out that I'm unknowingly being unfair to any user. If the second case, I'll try to fix that, so feel free to comment about anything (related to this, I don't care if your cat had babies... Okay, yes I do, send me pictures. So comment only on stuff related to this, or pictures of baby cats.)
And I do want you to comment on this. Both Showdown and PO have disconnect problems. I was wondering if people would think it fair that if the Gym Leader/E4 member has a four Pokemon lead over you and the service disconnects, then the battle falls under the favor of the Gym Leader/E4 instead of a rematch?