For the two-variable case, what are the practical differences between using the Engle-Granger procedure versus the Johansen test for cointegration? Is one universally more powerful than the other? Will one give more false positives or false negatives than the other? Should Johansen always be preferred?
Neither. This question and its references suggest that the Philipis Ouliaris (1990) test is a significant improvement over EG ADF and JCT. Given the automation, you should probably run all three tests and see if there's any consensus.
It actually surprises me there isn't (at least in Eviews) a function that shows a table of the EG, JCT, and PO results next to each other for comparison. This is how the lag selection table is presented, which makes it easy to find consensus in the criteria.
As always, however, I'd like to echo a statement made in the question linked above:
"The main question is whether you use the correct specification of deterministic components and lags. Using a badly specified test will probably be more harmful than using a 'bad' test on the correct model."