covariance matrix vs correlation matrix

#1
Dear all,
I am now studying PCA/FA and stumbled upon following problem: if variables are measured on different scales it's reasonably obvious that we should use correlation matrix. But, when one should use covariance matrix if variables have the same scale?
Jolliffe wrote that there might be problem with different variances (meaning, variables with biggest variances will dominate first few PCs). What else?

One more (stupid) question concerning correlation matrix - when we standarize variables we "lose" information about variances (they're all set to 1). What is the basis then for deriving PC's if variables are standarized (have the same variance)? I have a feeling I lack something very basic here :eek: