Hi,
As you say, adding a highly correlated variable should add very little new information, so one would expect similar performance for the two trainings. However, as this stack overflow answer discusses:
When adding more features the dimensionality of the fitting problem increases. If the input space is large in comparison to the number of data points in you training data it can be difficult for the method to find a good solution. (Curse of dimensionality.)
Cheers,
Kim