If you are trying to figure out the proteins' evolutionary history (e.g. if they are homologous) then you want a global alignment. In fact, there are very few cases where a local alignment is better, local is usually done only because it is far more efficient and less computationally expensive than global. But with tiny sequences of just as few residues such as the ones you have, you would want global almost every time.
The only case I can think of where you might prefer local alignment is when you have sequences that share little overall sequence similarity but you suspect they carry some sort of shared motif. For example, in proteins, that could be a protein domain. In that case, you would want to do a local alignment (possibly using something like blast) to identify those sub-regions of higher similarity.
Note that simple sequence similarity isn't really enough for you to decide whether they are indeed homologous. A more sophisticated approach such as psi-blast or HMMER will give better results. Nevertheless, a simple alignment will help you at least discard some obviously non-homologous sequences.