Both sentences involve a form of ellipsis called comparative deletion. Unlike some other forms of ellipsis, comparative deletion allows the omission of non-identical verb, for example am/are, so the section in brackets in the following sentence can be deleted:
I am better adapted to the climate than you [are adapted]
This sentence would never be written in full, but it could be written with or without [are]- it's a question of personal style which you would choose and, for a particular person, might depend on the context.
The streets of London are cleaner than New York [is clean].
This sentence is grammatically correct, but there may well be a semantic error, because it compares the streets of London with the whole of New York.
If the intention is to compare streets with streets, this could be done in two ways:
The streets of London are cleaner than New York's [streets]
The streets of London are cleaner than those of New York.
Note the apostrophe-s in the first version. The second version is more formal the first.