PCA is a process of projecting your matrix onto the eigenvectors of the covariance matrix of your data. There is one to one correspondence between eigenvectors and the principal components. It is a transformation which provably and optimally transform your data to a space from where you can recover your data, removing some(highest indexed) columns/rows, with a minimal loss in the energy. This means there exist no other algorithm which preserves the energy more than PCA.
When I come to your question, yes there are variations inside the principal components. The second principal component can have some values which are greater than some that of the 1st component. One can order them and take the N greatest of them if the eventual interest is classification and highest values are the primary factors. In general this is not always the case. The drawback of this idea is that only some elements corresponding to a principal component will be evaluated. In terms of data compression, this makes definitely no sense, however might be useful for classification. The biggest problem is that when you sort them and take the most significant N of them, what about the second data??? The indexes of the most significant values will be different! As a result your classifier will suffer from this mismatch.