Commuting bike with the bowed top tube Those asian bikes that have the curved top tube? What are the pros and cons of having that kind of frame design? Are they uncomfortable in really long rides? Do they flex or bounce too much? In comparison to a more traditional frame geometry.

They sell those really cheap here and they seem to be bomb proof.
Its called a "step through" frame, and was initially intended for women wearing skirts.  Notice the skirt guard in the upper-left corner of the rear wheel.

There's no connection with Asia at all, would have originally been English and European.

The curve of the top tube does allow a little more flex, damping out vibrations a bit more. 

As for comfort - it really makes no difference.  There's probably a fraction more side-to-side flex than a high top-tube diamond-frame, but the added damping is a positive.

Really cheap and bomb-proof are likely to entail a lot of weight by using additional metal.  That alone might make for a heavy ride.