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We compare the limit performance of asynchronous DS-CDMA systems based on different sets of spreading sequences, namely chaos-based, ideal random, Gold codes and maximum-length codes. To do so, we consider the Shannon capacity associated to each of those systems that is itself a random variable depending on the relative delays and phases between different users. The statistical features of such a random capacity are evaluated by means of the Monte-Carlo simulation of a proper adjustment of the classical formula for vector AWGN channels. It is shown that chaos-based spreading results in a nonnegligible increase of the capacity.