To be honest, I think many of us continue on to Muxia so that we can just keep walking.
But I know there is a historical basis that escapes my mind right now. The church on the rocky point is a spectacular location and is the source of its own pilgrimage, I've been told.
The only thing I would add about the choice between Santiago-Fisterre-Muxia vs. Santiago-Muxia-Fisterre, is that the although Fisterre feels more like an appropriate ending point to me (out at the lighthouse), if you walk Santiago to Muxia to Fisterre, you miss the Hospital - Fisterre part of the walk. That stage includes some walking on the moors till you hit the place where you can see the ocean and then descend to Cee. And there's a lot of nice beach walking on that segment as you get closer to Fisterre, which is very nice for those of us who live far from an ocean.
Frankly, I was surprised at how "inland" the Fisterre-Muxia walk was. Right before Muxia there was an option to walk through dunes and on the beach, but most of it is on small roads through rural developments. And now that the death-defying hop across the river has been eased by a real bridge, all the fun is gone!
so all this is to say there are pros and cons each way, and the only way to solve the dilemma,I guess, is to do a complete circle -- Santiago - Fisterre-Muxia-Santiago and see it all.
buen camino, Laurie