No they taste more or less the same. It is mostly a matter of the hen's diet and coloring.
Here's a tidbit for you though: fresh eggs need to sit for several days before hard boiling them. Otherwise you'll have a hard time peeling the shells off because the outer membrane will still be very strong. If you let it sit a few days that membrane begins to weaken and won't tear apart the inner membrane (egg white) when you go to peel of the shell.
