Unlike regular ishi that come in full-convex shape, Chinese stones are flat on one side. I found those stones difficult to work with, as they are not easy to pick up from the board. Granted, they lay more solid on get shifted out of place less easily.
Is this the only reason, though? Why do only Chinese people use this kind of stones? Is use of those stones in decline, possibly?
From the manufacturing standpoint, a few thousand years ago it was easier to produce stones that were convex on both sides. Before the Tang dynasty, because of this, all the stones were convex on both sides (just like ishi stones).
During the Ming dynasty, crafting skills progressed and stones could be shaped with 1 flat side and 1 convex (good for stability).
Japan imported the game of Go during the Tang dynasty (at that time the stones were all convex on both sides) and since Japanese are attached to their traditions, it stayed like this until now. (Which doesn't mean that the quality is inferior, it's just to stick with the tradition.)
With the years it also became fashionable.
For some people, Japanese stones make a better sound on the board, are easier to manipulate or are just pleasing to the eye. For others, Chinese stones are more stable and can be used on both sides to make temporary moves.
source: http://zhidao.baidu.com/question/265925385.html
PS: To answer your last question, the use of those stones is absolutely not in decline.
One nice property of half-convex stones is that there are two distinct ways to put them on the board. This is often used to play out variations.
