MCCA is a extension of CCA through tensors, according to authors this is due to their inter-subjects variability and effects of ongling EEG and noises.
The basic difference is between CCA & multiway CCA ,both are multivariate statistical method to reveal correlation former two sets of vector variables (two sets of data) & later two multiway data arrays .MCCA achieved heigher recognition accuracy than CCA .
For giving more info; (If you are working on SSVEP) the reference signals in MwayCCA are chosen a lot better than CCA, and it increases accuracy and ITR.