I was wondering what are the differences between a small (20'") trial bike and a BMX? Were I to choose one to buy, what should I consider before I make my decision?
Here are two bikes that are reasonable examples of each category (notice the handlebars, the different sized chain ring (i.e. gear transmission ratio), the seat post and the brakes).
The riders are doing seemingly the same trick. But the trial bike stands still like a rock and could stay in this position forever (strong brakes, static equilibrium), the BMX rider is on top of this obstacle only for a few seconds, not needing to use his brake (dynamic equilibrium, notice the fast spinning front wheel):
As for which you should choose, well, I guess it depends on how you intend to ride (and whether you think a bike without a seat is ridiculous!).
I'm not sure on the frame geometry of trial bikes but it looks like they have a very short "top/down" tube and the handle bars are nearly over the front axle. This gives you very poor handling at high speeds, hence the slow technical balancing riding that is done on them. Basically, they only have tire size in common...so which to choose depends on what you want to ride.