I think Senator Lieberman probable accomplishes more behind the scenes as a private Senator than allot of the very public Senators, who are lightening rods. As a quite private (by private, I mean not allot of free media attention) Senator he can build bridges and facilitate compromises with his colleagues in the Senate. Something that Senator Clinton or Kennedy are not able to do because many on both sides of the isle do not want to be publicly associated with them by their critics back home.
You are absolutely right. People give added weight to those who have served our country and have had to do the actual heavy lifting of those policies and orders from Washington DC.