+1 not 100% certain about the design of the ring between the 2. It isn't always about getting a brighter output on the bulb. The light still needs to be efficiently diffused through the entire ring to give you that newer fresher look.
I updated mine from normal to LED and it isn't brighter but the colour of the light temperature has changed. Not stating that the same will apply to you, but merely mentioning what I have experienced.