"Wake up Joe" or "Wake Joe up"?

Either can be used in many situations, but Verb Noun Adverb is the common order for all of these.

Put the jacket on. / Put on the jacket.

Pull up your pants. / Pull your pants up.

But sometimes the reversal doesn't work because the preposition seems to apply to the noun rather than the verb.

Get your clothes on. / Get on your clothes.

Work the lotion in. / Work in the lotion.

In the second versions here, you might be telling someone to stand on top of their clothing or work while covered in lotion. Certainly it is fine to say "Put on your clothes." It all depends on the verb being used.

Other times it would sound odd to reverse the order because the preposition means something else depending on the order:

Get the lead out! / Get out the lead!

The first means get moving more quickly; the second means to furnish forth some quantity of lead you may have.

"Wake up Joe" and "Wake Joe up" are both OK, and as you say the second flows better. But if a pronoun is used then the second form is not only better, it is compulsory: "Wake him up" works, but "*Wake up him" is ungrammatical.

This is almost always the case when the preposition in a phrasal verb is used as an adverb rather than strictly as a preposition... e.g. here "up" is an adverb because it specifies the "direction" of the waking, rather than applying to Joe specifically...

As an alternative to this 'either/or' scenario, I would suggest eliminating the word "up" from the phrase entirely. The result is perhaps more traditional, but I don't believe the word "up" is necessary in the example phrase, nor is it needed in most cases.

1. "Go and wake Joe."
2. "The drunk woke upon hearing the door slam."
3. "I must wake at dawn in order to arrive on time."

Whether we are performing the waking action (transitive, Ex 1&3) or simply describing the waking (intransitive, Ex 2) the word "up" is not necessary. My understanding is that "up" came to be used because of the associated phrase "get up", as in "I got up in the morning".

One would not use "up" alongside other synonyms for most "waking" situations:

1. "Joe rose from his drunken stupor." vs. "Joe rose up from his drunken stupor."
2. "I must rise at dawn." vs. "I must rise up at dawn."

In these cases, the former sounds clean and proper, whereas the latter sounds a bit like the subject is rising from the dead or preparing for battle. I'd like to see more discussion on this topic, as I have also done searching outside of this forum and have had a hard time locating other opinions.

I would suggest the difference is one of emphasis. In the case of "wake up Joe", the implication would be "wake up Joe", rather than, say, put a mouse in his bed. In the other, "wake Joe up", it would mean "wake Joe up", rather than any of the other drunks lying around on the floor.