Both seem to be in common usage, but is there a nuanced difference about when one is more appropriate than the other? Thanks.
They're both forms of the same thing, a verb-particle idiom sometimes called a "phrasal verb":
I sped the video up. I sped up the video.
But if the direct object is an unstressed personal pronoun, up has to come at the end:
I sped it up. *I sped up it. (ungrammatical)
And if the direct object is very long, put up first:
?I sped the new program for rendering alpha and beta particles up. (awkward) I sped up the new program for rendering alpha and beta particles.
Otherwise it's difficult to understand.
There really is no difference; it is a phrasal verb (a verb consisting of both a "main verb" and a "prepositional particle", which combine to have a different meaning than the verb alone), and a phrasal verb can be joined directly or split, depending on the object. The only hard and fast rule regarding splitting up a phrasal verb is that if you use a pronoun as the object, the pronoun MUST split the phrasal verb:
good: I want to speed the engine up
good: I want to speed up the engine
good: I want to speed it up
wrong: I want to speed up it
Otherwise, the primary guideline is, try not to put the particle so far away that it's hard to recognize that a phrasal verb has been used; see this ELU question about splitting up phrasal verbs for more info.