You may find yourself using certain expressions in a comparison essay. They are listed here, for your convenience, so you will use them correctly. Besides common words such as "but" and "however" which show transition and contrast, you may use these expressions:
Cats are lazy. In contrast, dogs are livelier.
In contrast with cats, dogs are livelier.
Contrasted with cats, dogs are livelier.
Cats are lazy. In comparison, dogs are livelier.
In comparison with cats, dogs are livelier.
Compared with cats, dogs are livelier.
whereas or while (do not put a comma after these words)
not as . . . as (Cats are not as fun to play with as dogs)
different from or different than
distinguish from (A cat's diet is distinguished from a dog's diet by its high protein content)