Now this is my kind of topic.
Before I can start my argument, I'd like to bring up the following simple fact: Bill is intelligent, regardless of any sort of accident with a costume (which he probably wouldn't have known about without actually trying the costume on first anyway) or Teleporter (which could have really happened to anyone). Now, why do I say this? It's fairly simple, really:
1. In the games, he invented not only a matter teleportation/storage device but also a matter teleportation device that can transmit said matter across time. I'd like to see someone of his age do that without a Flux Capacitor and a DeLorean. Same thing goes for the Adventures version, lax the Time Capsule.
2. The anime version has been complimented by Professor Oak himself. In fact, in Oak's own words, "Bill is a young Pokemon researcher who knows even more than me. See what you can learn from him. He can teach you just about anything about Pokemon... and then some." Although Oak is kind, I really don't think he'd reward someone who didn't deserve such a reputation with such praise.
3. On the Dragonite thing: It was the dead of night with thick fog blanketing everything further out to sea. I don't think even Professor Oak would be able to identify that Dragonite, and I wouldn't expect Bill to be able to just by its call, considering the fact that the episode's Dragonite sounded absolutely nothing like what Dragonite is established to sound like later on in the series.
4. With that said, the anime Bill also has the ability to interpret a Pokemon's call with only a vocal recording to work with. He can also theorize what a Pokemon may be like just by wearing a costume. In other words, he's well-versed in Pokemon psychology, at least.
5. The Adventures version also has the ability to distinguish what move a Pokemon will use just on the stance it takes mere moments before the attack is executed (i.e. Fearow).
6. Toshihiro Ono's version is a skilled inventor working for a prestigious technology research center (which is responsible for everything from new versions of the Pokedex -- which he did lend a hand with in that particular manga -- to new Poke Balls, which he labels as "antiques").
7. In the games, he indexes his own Pokemon. As in, he's made his own Pokedex.
Therefore, consider everything Bill has done before calling him stupid. He's actually smarter than most people like to think, and the only reason why everyone thinks he might be a little dense is because they can't see past one (or, in the case of the anime, a badly interpreted two) instances. If you're thinking, "OMG! HE COULDN'T IDENTIFY A DRAGONITE!," then go outside on a dark night when there's thick fog out and try to see ten feet in front of you. Then imagine that the Dragonite is actually double that distance away from Bill at the time he's always tried to identify it (and he says that it only comes on foggy nights in the episode), and you'll see what I mean.
And to Usohachii, then why didn't Oak? Remember, Oak's at least forty years older than Bill. He had plenty of time to think of the Teleporter, so it's hardly something to hold over Bill.
With that said, oddly enough, though I'm admittedly a Bill fangirl (hence why I've taken the time to analyze his incarnations for enough proof to say that he's not exactly stupid), I'll have to say they're equals. Why?
Because Oak has at least twenty more years of experience than Bill. On the other hand, Bill has enough knowledge to be considered a rival towards Oak. It's wisdom-intelligence versus ingenuity-intelligence in this debate. The mentor versus the student.
Oak is the typical kind, old man. He's invented the Pokedex, but he can't fill it on his own. He can be a little critical (i.e. whenever he used to compare Ash to Gary), but if a trainer needed advice, he's just a phone call away. He's seen pretty much everything in his lifetime, or he carries himself like he does. (Then again, this was also the guy who's seen Celebi, so it wouldn't be surprising if he did.) Bill, on the other hand, has enough book smarts to know how to send a Pokemon through time, interpret behavior based on a voice recording alone, and figure out what move a Pokemon is about to use, but he just doesn't have the same edge just because he hasn't experienced the same amount of the world that Professor Oak has. That's really the only one-up Oak might have on Bill, though when it comes to intelligence alone, it's still a tough call.
Edit: Correcting a quote. Whoops.