Yes, the flavours will change... different peppers do different things, and everyone has their preferences.
Generally (like a fruit) the riper, the sweeter or fuller the flavour. Some people say that the heat also increases with ripeness, others say that heat peaks when the pepper first ripens. I have a friend how swears up and down that his Scotch Bonnets are at peak heat when the pod reaches full size, but hasn't started ripening yet.
I haven't really experimented with the heat levels, but like the flavour of a ripe pod.