All alternatives are perfectly natural, and it would be overscrupulous to suppose any difference in meaning (or even fine nuance of meaning) attaches to the choice. But the general principle is always simpler is better / less is more, so I suggest you stick with the majority of native speakers...
It might just be worth pointing out that you can break [some complex entity] up (or ...down) without actually specifying the "lower level parts" that would thereby result. As the results from this NGram for break the problem [nothing / up / down] and show, if no such "resulting smaller parts" clause is specified, the most common "phrasal verb" form is break [something complex] down.
For contexts where the "smaller parts" are unspecified, you must include one of the prepositions. It's natural to speak of cracking a problem (solving it), but you wouldn't normally crack a paragraph unless it was some kind of cryptic text that you'd successfully decoded.
It's an extremely fine nuance, but I think I can reasonably say that to break X up is more natural when focusing on the end result being that X ceases to be the "coherent whole" that it was. Whereas to break X down works better when focusing on the smaller parts that will thereby result.