Your chocolate cake looks as beautiful as your opponent's, but unfortunately, you didn't bake it as carefully as he did.

For the first blank, "look" is a linking verb, so it describes the cake itself. We need the adjective beautiful.

For the second blank, "bake" is an action verb, so we need the adverb carefully to describe how you baked it.

In both cases, the structure for equality is always as + base adjective/adverb + as. We never use "than" or comparatives like "more" inside this structure!