Of the past is an adjectival phrase, but in the past is an adverbial phrase. So your first sentence, if you substituted one phrase for another, would have different meanings. To say that "phones in the past were landlines", which contains the omitted verb "used" before "in the past" does not suggest that modern phones are landlines, but "phones of the past were landlines" says that those which have survived in someone's basement still are landlines.
This is implicit in your second sentence fragment (which is not a complete sentence), since presumably the rest of the sentence compares transportation in the past to transportation today, and either discusses the differences between them or establishes similarities - but either way the two classes of transportation are assumed to be different. If they were not different there would be no point in comparing them. But "transportation of the past", such as horse-drawn carriages or steam-driven locomotives, has not changed today, although it may not be used much.