What's the word for comparing someone to a famous character or person?

Question

For example, when someone dresses with colorful and flashy clothes and you say "Who are you, Liberace?".

Or when someone says something smart and you say "Woah, hold it there, Brainiac!".

Answer 1

This is called an archetypal name, which is a type of antonomasia, which is a kind of metonymy, as noted in KarlG's answer.

Archetypal names are proper names of real, mythological, or fictional characters that have become designations for archetypes of certain personal traits.

Examples include:

• A womanizer or latin lover may be called "Casanova" or "Don Juan".
• A romantic guy may be called "Romeo".
• A genius might be called "Einstein".

Answer 2

Substituting a proper name for a quality closely associated with it is an example of metonymy. The associated adjective, however, is metonymic or metonymical.

One of the most famous examples occurred during the US vice-presidential debate in 1988 between Sen. Lloyd Bentsen (D-TX) and Sen. Dan Quayle (R-Ind.). After Quayle had mentioned President Kennedy, Bentsen, after a brief build-up, told Quayle “You’re no Jack Kennedy.” It didn’t matter what quality or qualities one associated with the assassinated president; Quayle, Bentsen implied, was devoid of any or all of them.

The proper name need not be that of a person:

The climb-down from New Coke left Pepsi's Roger Enrico crowing: “This is the Edsel of the eighties,” he said, referring to the greatest flop in the history of the American car industry.

Edsel Ford was of course the name of a member of the Ford family, but more notably a model of Ford named for him that was a tremendous commercial failure.

Or a place:

Despite a spate of recent development, Fiji is no Tahiti, where development stacks upon development.