Yes, Kennedy Center Honors are on the same level as the British Knighthood, because it is the best thing that we have to honor people who are highly accomplished. British Knighthood is given by the government. We do not have that, but we have the best award that you can be given for outstanding achievement in the United States.
Much has been made of the Kennedy-as-Camelot comparison, and the metaphor holds true today. Despite some of their moral failings, the Kennedy family represented the best we could achieve as a nation, and giving someone like an entertainer the Kennedy Center Honors, does in fact reflect on national character and ideology in a near-identical way to British Knighthood.
A knight of the realm is bound by loyalty to head of state, i.e. the reigning monarch. Random artists would have no reason to pledge their loyalty to the president of the U.S.A.
That aside, knighthood is tied to the ideas of nobility - agricultural pre-industrial society. If the U.S.A. is truly a modern, liberal, universal democracy, there should be no such concept as "royalty" and "knighthood". If freedom and equality are what you value in a society, monarchy and it's related ideals are to be opposed. I am a citizen of the first modern European democracy, and we killed our royalty.
Being knighted by a reigning English monarch has no equal anywhere in the world. The reason is that no monarchy is as closely watched as the British Monarchy throughout the world. More people cared about the birth of Prince George than whether or not someone in the Spanish royal family had a baby. The Kennedy Center Honors are nice, but those are just for the arts. A knighthood can be for any facet of British culture.
I do not believe that the Kennedy Center Honors are on the same level as the British Knighthood. I think that while it is a great honor, it doesn't have the history and prestige that a person who lives in the UK will get from a Knighthood. I think that it is an honor thought to get either one.