They are near-synonyms, but you cannot always interchange them (as a rule, if a prefix is prepended to a word, then its meaning is modified - at least a little bit). Εκμάθηση is more associated with the process of learning, not the concept of learning. As Evelina explained, you may say that "Η εκμάθηση μιας ξένης γλώσσας απαιτεί μεγάλη προσπάθεια" - this refers to the process of learning - you may, however, also replace the work "εκμάθηση" with "μάθηση".
What is more, you may not say "δια βίου εκμάθηση" (lifelong learning). Instead, you should say "δια βίου μάθηση". There are several other standardised phrases where you would use "μάθηση" instead of "εκμάθηση". For instance, if you are familiar with the term "learning curve", in Greek this translated to "καμπύλη μάθησης".
But to cut the long story short, if you're not very advanced in Greek, I think you should go with "μάθηση". It will work for you in most of the cases.