There are a few differences between the two sentences.
Omission of that
One is that one form omits the subordinating conjunction that, which as I pointed out in the comments is addressed in this question, and which funnily enough I'm just after answering about a further case. From there we can see that that is optional here; you could just as well swap the decision and have "Attach any material that you need included" or "Attach any material you need to include".
So on this point; both are fine.
Predicative Clause vs Infinitive Clause
Another is that in one you use "included" while in the other you use "to include".
As Edwin points out in the comments, the first omits "to be". Let's leave consideration of that omission for now, and think about the difference with the copula included. Let us consider:
The material was included.
This structure (subject, copula, past participle) is sometimes called the "false passive" because one can parse it as being a passive-voice clause (with an active equivalent being "someone included the material"), but it is generally taken as using the past participle as an adjective in predicative use (compare "the included material" to show how included can be adjectival and "the material was excellent" to show how the structure accepts an adjective).
As you can see, while there is an ambiguity as to just what way this structure works, the two ways of considering it amount to the same thing, and "a difference that makes no difference is no difference at all".
Now, since that predicative clause describes a state (of being included) it can be used with need to state its necessity:
…you need to be included."
Meanwhile the alternative "…you need to include" uses the to-infinitive to indicate an action that is required. It's normal with this form to not repeat the subject if they are the same in each case, hence "you need to include" not "*you need you to include".
Between the two, ("…you need to be included" and "…you need to include") there is not an exact equivalence. The former doesn't say who does the including, so we could just as well interpret it as equivalent to "…you need me to include" or "…you need the printers to include", and so on.
This amounts to the same thing though. And again "a difference that makes no difference is no difference at all".
So on this point; both are fine.
Omission of to be
At this point we've shown equivalence between one of your sentences, and a similar sentence:
Attach any material that you need to include.
Attach any material you need to be included.
The second differs from yours in that yours omits "to be", and we aren't truly comparing them until we can justify or condemn that omission.
This is probably the trickiest element here. Such zero-copula is rare in English, particularly formal English. It's most common either in set phrases ("the more, the merrier") and informal use. It's also much more common in some dialects than in others (AAVE uses it heavily, for example).
It is more acceptable, even in formal use, in short dependent clauses, but it's really hard to say why (I welcome comments or other answers addressing that). A significant factor is no doubt that being such a short dependent clause, there's no scope for confusion.
And so on this third point, again; both are fine.