So it looks to me, based on this question over on StumbleUpon's support site that there's a bit of a downside in terms of one aspect of SU, from a SU employee:
Sorry, we can't redirect existing
reviews to new urls, nor change the
entry details for existing reviews.
You may wish to ensure that you have a
redirect on each of your "old" pages
that have been reviewed, so that any
visitors following that route end up
at your new content.
So basically changing the URL will disassociate the existing reviews and stumble data from the page. Now, users can still get there (assuming the redirects are done properly on the server), but there is a downside.
But based on what I see of some sites that implement redirects, there should be no downside from changing the url. Still, I think I'm planning to not play with this for existing pages with high traffic.