When there are only two repeated measures, the univariate and multivariate analyses are equivalent. When there are only two treatment groups, this reduces further to Student's t test for independent samples. It would be constructive to take a small data set and verify this by using a statistical program package. In my experience, this recommendation is too simplistic. When the tests disagree, it can be due to an outlier, or that the requirements of one or both tests are not met by the data, or because one test has much less power than the other.
Further study is needed to determine the cause of the disagreement.
I tend to agree with Wilkinson. However, in some studies, the reduced number of degrees of freedom for error in the multivariate approach may cause it to fail to identify effects that are significant in the univariate analysis. In practice, repeated measures analyses can raise more questions than they answer, especially in situations where researchers take many routine serial measurements. However, many of these interaction will be of questionable biologic importance and difficult to interpret. For this reason, it is usually better to construct a simple summary of the repeated measurements based on biologic considerations and analyze the summary by using multi-factor analysis of variance.