Sequence comparison is a fundamental step in many important tasks in bioinformatics. Traditional algorithms for measuring approximation in sequence comparison are based on the notions of distance or similarity, and are generally computed through sequence alignment techniques. As circular genome structure is a common phenomenon in nature, a caveat of specialized alignment techniques for circular sequence comparison is that they are computationally expensive, requiring from superquadratic to cubic time in the length of the sequences. In this paper, we introduce a new distance measure based on q-grams, and show how it can be computed efficiently for circular sequence comparison. Experimental results, using real and synthetic data, demonstrate orders-of-magnitude superiority of our approach in terms of efficiency, while maintaining an accuracy very competitive to the state of the art.