It has to be a motorbike...

Having just been to the Philippines (and I imagine many southeast Asian and over populated areas are also like this), Motor biles are everywhere and small enough to slip between cars, yet large enough that a car won't hit you because your going to damage it.

In particular, I would recommend a Dirt Bike because it has the capabilities for you to perform more stunts which would be great in making everyone in traffic hate you as you drive over their cars.

Firstly, there is no way a Car, Tank, truck or large vehicle would be able to win. While they can force their way through traffic, in dense enough traffic conditions they have to compete with other large vehicles or equal caliber. They will also face problems when turning and have slower acceleration times and speed limits since it takes them so long to accelerate up to speed and slow down (they can't go too fast or they won't be able to stop if they get cut off or make a turn).

For cars in particular you can image that they aren't really going to come out on top. Just go stare at some peak hour traffic and you will understand why. 

Animals also aren't going to work well. Animals are smart enough to know how to get out of the way and vehicles could easily force an animale (horses mostly) into a very dangerous situation by slowly pushing up towards them or into the side of them to force their way out. Your horse will also be freaked out by the constant noise and honking. Thats also combined with the fact that a horse isn't going to work over larger distances or be nearly as fast as a normal vehicle and still simply stop walking when it needs to take a piss in the middle of the road.

So it comes down to our 2 wheeled friends, Bikes, scooters and Motor bikes. What about 3 wheeled vehicles? well they are larger than 2 wheeled vehicles which means in dense traffic conditions they will need to be more carefule and can't slip between the gaps a 2 wheeled vehicle will. In addition, most 3 wheeled vehicles end up being modified versions of 2 wheeled vehicles (I swear the only ones I've seen are basically bikes with an additional cart added or the back wheeled switched for two, or the unstable one that falls over from Mr Bean). 

Scooters and Motor bikes push out Bicycles simply because they are motorized. They will be able to go faster for longer  and while they might not be able to squeeze through the smallest of gaps, your going to be able to comfortably move 10KM, 50KM or 100KM easily on a motorbike when compared to a manual bike (There are no road rules, so bike lanes are basically lanes for any vehicle now).

So out of a Scooter and Motorbike, I would say scooter wins simply because its cheaper. It can make riskier moves because you don't need to worry as much about replacing/repairing it. 

I still recommend a Dirt Bike, simply because people use it to perform stunts. You could for example, get yourself ontop of another vehicle and ride over it, or just sit there for the ride while it takes you to the location you want.