You know, you come to a tricky one. And we need to bring another one up:
Let me in/out/through. <<< Adverb. (as in "figure it out/figure out it" >>> "let in the dog"/"let the dog in")
Want me out. <<< Adjective.
Why? How about "I want you dead", "I want you happy", "He wants it as cheap as possible". There is this rule, the "to be" is allowed to omit in "want object to be adj", personally I think it is kind of formal grammar as it has made its presence in some quite serious tests. So that's kind of like, "I want you to be out of this", although merely "I want you to be out" would sound bad, I admit.
If that's not convincible enough yet, see if this helps:
You let me bad(ly). (mumbo-jumbo, should clarify that mostly "let" only works with so-called "directional adverbs" like "in/out/through/on/up/down", quite a complex word itself, still referring to some exceptional and arguable cases like "let go", "let alone", "let someone in/into/through something", "in/..." as prepositions, etc, etc)
vs I want you bad(ly). (real adverbs, see the semantic difference in contrast to "I want you out", assuming "out" is an adverb)
But here's the real dilemma: How'll my theory deal with "I want out" (which can indeed be frequently heard in colloquial speech). Can't say it's adjective here since "I want happy" is completely nonsense, and no such rule as "to be" can be left in "I want to be happy" (note "more" is a noun in "I want more", though, surprisingly). That beats me. Now check this out: