Whew, you don't ask easy questions! In brief and in general: the Yang style is derived from the Chen style. The Yang style places emphasis on open, expanded postures and flowing, even, graceful movement. A main focus of Yang style is "peng jin," which is difficult to describe but is the type of energy you might feel if you tried to push a beach ball down into the water of a swimming pool. The Chen style is more obviously martial and contains more vigorous movements, including fast punches and kicks. A main focus of the Chen style is "chan ssu jin," or a coiling type of energy. Neither is easy to learn; they both demand a lifetime of study, and they are both well worth it. In my opinion, unless you are sure that a particular style is absolutely the only one for you, it is much more important to find an excellent teacher. He or she will make the art interesting and rewarding, regardless of style.