I've found staves to be more robust in general. They break less during the build and seem to outlast board bows in general.
I've worked with hard-maple, hophornbeam, pin cherry, white ash, and yellow birch in stave form. And I've worked with white oak, hard-maple, black cherry, hickory, and elm in board form. I've made half a dozen board bows, and nearly two dozen stave bows.
I've exploded about the same number of board bows as I've completed, and retired a couple finished board bows due to ticks or cracks that they've developed over time. I've yet to explode a stave, but I have had a few take so much set as to be useless. To be fair though my stave bows are all newer and probably have not been shot as much as some of my board bows.
I don't think there is a difference in the performance of the final product, but I do think there is a difference between the durability and reliability of both the unfinished and finished product. This is in general of course. There will be some board bows that last longer than some stave bows to be sure. It seems there are always exceptions to every rule in this craft. But on the whole I think stave bows stand the test of time better.
I will admit that I havn't been doing this that long though. And I made my stave bows with more experience than I did my board bows. But overall I trust my stave bows more and I don't see myself returning to boards any time soon.