This depends what is being tested. For small samples and multivariate tests (ie anything more than two variables) the Johansen method is better. But for bivariate testing of typical runs of financial price data the Engle-Granger method has certain advantages. For example, by using a criterion of minimum variance (as opposed to the Johansen criterion of maximum stationarity) the method lends itself far more to risk/portfolio management applications. For a fuller discussion go here to read Professor Carol Alexander’s Optimal Hedging Using Cointegration paper.
It may also be worth pointing out that the Johansen method has its own drawbacks: sensitivity to lag selection, how to select the best cointegrating vector, ambiguity in the presence of conflicting t-values and (according to the Michael Wickens critique) a tendency to signal cointegration where none exists.
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