cpu/gpu have some effect on streaming, but nowhere near as much as your internet connection. i ran an older phenom II to stream, and it streamed things just fine. the internet connection itself determines how the stream looks when it is broadcasted. as i listed before, use the speedtest link, and check your upload speeds. if it is under 5mbps, you wont be able to do 1080. 3mbps, might get you 720p.
if you upload speed is low, you would have to lower the bitrate of the uploaded stream, which is what lowers the actual quality. the goal is to have it stream at the native resolution that you see, but is not always possible if your internet is garbage.