Forward checking vs arc consistency on 3-SAT
Both forward checking (FC) and arc consistency (AC) are methods of inference. Regardless of the problem you are solving, choosing a specific method of inference is always a tradeoff. Basically, the more you are willing to pay in terms of time, the more you gain in terms of strength of inference. So yes, it is faster to perform forward checking than arc consistency, but arc consistency is more effective at pruning the search space. If you are willing to pay even more, there are even stronger forms of consistency. The book by Russell &amp; Norvig gives a nice, quick introduction.

Both FC and AC are relatively cheap and easy to implement, too. The suitable choice depends on the specific structure of your problem. I think at least in general, it is best that you experiment with both.