Well, I'll field the flatland end of it, since these two clearly aren't flatlanders. BMXTRIX might have some additional wisdom to add.
Flatland frames are typically made out of the same 4130 as everything else in BMX. Aluminum and titanium frames are not common (and IMO not really worth it), but they do exist. Bikes and componentry in flatland are usually lighter because they *can* be and get away with it. Pegs are larger, knurled for standing and made out of aluminum instead of 4130 (or in some cases 4140) steel because they don't take much abuse from stalling or grinding. Forged aluminum cranks are commonly preferred for stiffness and light weight. Radial (uncrossed) spoking is common on the front wheel and 36 spokes are usually used over 48 because not only are the wheels lighter and the extra strength unnecessary, it's easier to get your fingers in the spokes if they're spaced further apart.
Freecoasters are much more common in flatland than in street, and are almost unheard of in dirt. This is a type of hub that can be disengaged by pedaling backward 1/8-1/4 turn, allowing the rear wheel to spin freely forward and backward without turning the pedals. They are relatively heavy, expensive and can be tempermental.
The biggest difference between a pure flatland bike and those designed for street, park and dirt is in geometry. Flatland bikes are EXTREMELY compact, the average top tube being right around 18.5"-19" and rear ends in the 13.5" range. Head tube angle is usually very steep (76 degrees is common) to accommodate quick turns at low speed, and down tubes are either gusseted or bent up out of the way of scuffing the front wheel.
Price is not a factor of complex design or exotic materials nearly so much as it is a factor of availability and limited production. Flatland isn't a huge moneymaker in the States, parts are made in limited quantities by small companies unknown outside the flatland world. The fewer units produced, the more you have to charge to stay in business. Simple economics.
As for the others, bikes intended for street typically take the most abuse and are typically the most overbuilt. Compact geometry for technical lines might be preferred over longer top tubes and more relaxed geometry for flow in park and dirt. As a general rule...longer bikes, relaxed geometry = more stable at higher speed, forgiving on large tricks. Tighter geometry = more agile, better for technical moves at lower speeds. There's no real recipe for any of these bikes. You can blend characteristics, mix and match parts (say putting a freecoaster on a park bike or using a longer frame for flatland and street) to fit YOUR riding style. Locking yourself into one kind of 4 kinds of riding is stupid.