"Jihad" also has a much-broader meaning than "crusade" without needing to reach into figurative senses of the word, which colors the whole thing rather differently.

[EDIT] Oh, and the book pretty clearly draws fairly heavily from Lawrence's Seven Pillars (at least a couple scenes or sequences are practically lifted from it, aside from the general vibe and structure of an untested officer from lush England being sent to a distant desert, proving himself among the locals, gaining insight during a nigh-fatal fever, and playing a major role in leading them against a superior occupying force while leaning heavily on the local forces' distinct mobility & supply advantages, with the ultimate goal and final culmination of the project in the taking of a major capital city) and downplaying the Muslim elements of the Fremen pushes that aside a bit, which is... fine, I guess, but not exactly an improvement.

But I do agree that that particular axis is one of the weaker parts of the adaptation. Though I'm not convinced personally it subverts the theme entirely; just maybe skips a few steps.