To me both ”役に立つ” and “役立(やくだ)つ” mean the same thing, “It helps,” or “helpful.”
When I consulted how to translate “役立(やくだ)つ” into Japanese with Kenkyusha’s “New Japanese English Dictionary” for a reference, it simply told “See 役に立つ.”
However, it appears to me there's a bit of difference between their usage and nuance. The former (役に立つ) is more often used in “predicative” form in a sentence than the latter (役立つ), which is rather used for “adjective” form in a phrase.
For instances, we say;
救急箱はいざという時に役に立つ – The first-aid kit is effective in emergency.
彼は役に立つ人間だということが解った – I found him being an able person we can rely on.
この芝刈り機は役に立たない – This mower doesn’t work.
果たして私、お役に立ちますか、どうか – I’m not sure if I am of any assistance to you or not.
英語の勉強に役立つ本 – A book helpful in learning English.
就職に役立つコネ – A connection helpful for job hunting.
問題解決に役立つアドバイス – Advice that helps solving the problem.
世間のために役立つ人間になれ - Be a man who is useful for the world.
Though I don’t have any academic ground, I think 役立つ derived from "役に立つ" as its contraction.