A box is not considered a shape in the same way a circle, triangle, rectange, or square are. In the given sentence, we would change these words to adjectives. For example: The initial impression he wanted to create from the shape of the building as a whole was rectangular. In the case of a box, we would have to use an adjective like boxlike or square: The initial impression he wanted to create from the shape of the building as a whole was boxlike or square. (Square being a noun and an adjective.) Therefore, to keep the sentence grammatically correct with the use of the noun, we include the phrase "that of". The initial impression he wanted to create from the shape of the building as a whole was that of a [noun].

They both mean the same. In the sentence "the shape of the building was that of a box" that refers to the word shape as in "the shape of the building was the shape of a box" and in order to avoid the repetition, that is used.