It really boils down to what you want to do with your bow. Do you want an all around bow that will do both well? If so then broad head tuning is what you should try. I wouldn't even waste time on bare shaft tuning, just go right to broad head tuning and work on that until you are happy.
I can't imagine tuning a bow to shoot a broadhead without messing with the spine. It's by far, the most critical aspect in my opinion. I use the bareshaft to test spine, and determine nock height - that's all, but it's critically important when shooting a broadhead.
I still think that when you end up with broadheads hitting in a significantly different spot, you missed something. The spine is incorrect, the FOC is too low, the bow has a problem, the arrows aren't spined matched, the broadheads aren't on perfectly straight, or some other critical area was missed. Of course, with some set-ups, the best you can do, will not allow them to impact in the same spot. Correct the problem with that set-up and they will.
Arthur, you're right, I've never shot field archery, but it sounds like fun. I do have a range in my yard that allows me to shoot up to 100 yards, which I shoot at every week. I have a very good handle on my relative group size at a 100 yards, but I don't actually measure them. If there was a problem with the group size, I wouldn't move my centershot. That was determined with my plumb line, which is the most accurate method I can think of. If I'm hitting a plumb line at all distances, how could group tuning improve the centershot setting on the bow? It can't. I prefer to test one vector at a time, which it why I shoot for a plumb line and then a horizontal line when setting nock height.