Correlation analysis deals with the association of two variables. Comovement analysis with the parallel evolution of entities in a time series. Correlations can be an indicator of comovement, Being not an economist, I would go for correlation analysis.
correlation analysis to examine the degree of closeness between the two variables while the co-movement to test the effect of changes between the variables for which data are experiencing volatility.
you should use the analysis of co-movement in eviews even better using panel data, price and different places. Correlation is not suitable for time series data that has a high tendency to fluctuate.