depends on your height. you should never get skis that tower over you. so if the 176's are a little bigger than you, 183 is a dumb idea. but if your kinda around 6 feet... go for it.
yes there is a difference. it depends on what kind of skiing you are doing. for park you might want the 176 and for pow or hardpack you probably want the 183. it depends on what you like though.
i ride 177 in park and 182 in powder and i notice a big diff in the skis speed, handeling and stablity, alot has to do with the demisions of the ski and the stiffness.