Sykes-Picot was concluded in 1916 actually only a few months after the conclusion of Hussein-McMahon.

The argument as to whether or not the agreements are contradictory comes down to an incredibly lawyerly defense that the British employed after the war which asserted that Hussein-McMahon's exclusion of "portions of Syria lying to the west of the districts of Damascus, Homs, Hama and Aleppo, [which] cannot be said to be purely Arab, and must on that account be excepted from the proposed limits and boundaries." They asserted that this exclusion of the territory west of these districts was consistent with a French Syria and non-Arab (later British) Palestine under Sykes-Picot.

I have not come across any historians who take this British line seriously. The plain sense meaning of what was promised in Hussein-McMahon was contradicted by Sykes-Picot and the later post-war settlement.

There are more interesting questions however, such as whether what was promised in Hussein-McMahon should be understood in the context of what was promised in Sykes-Picot, or Balfour, or any of the other war time promises. Just as the French did not get all of the territory allotted to them based on how the war transpired, nor did the Hashemites. As a transactional promise -- one independent Hashemite kingdom in exchange for one Arab revolt against the Ottomans -- a case could be made that the Hashemites did very well out of the deal given that the Arab revolt was less substantial than had initially been hoped.

The role of Sykes-Picot as a betrayal of "the Arabs" is another interesting question. By the entry of the United States into the war, the 14 points had been understood promising self-determination to the Arabs. But that's not really what Hussein-McMahon promised either. It promises a Hashemite Arab kingdom.

In any event that's another can of worms. The basic answer is that, yes, they contain contradictions, but these should be understood in the context of wartime promises the British were making with everyone and less as some kind of grand, calculated betrayal.

D.K. Fieldhouse's Western Imperialism in the Middle East is a good read on this.