As you've said, a stat PhD is much more flexible and does not pigeonhole your future opportunities as much. However, if you've found some professors you feel are a perfect fit for the type of research you'd like to do at Emory, then perhaps this is the better choice. I am not as familiar with Emory's biostat program, but I can speak more about UIUC's stat program. UIUC's program is definitely on the rise due to an amalgamation of changes: admin changes (Shao becoming PhD Director, Bo becoming dept chair), expansion of faculty (quite a few new hires each year), and the reconstruction of the old stat building. As @Nothalfgood mentioned, if you choose to do a stat phd, there will be a heavier theoretical requirement as opposed to a biostat phd; do keep this in mind. Of course there are always other things to consider as well such as stipend, location, hobbies, etc. Sorry I can't answer as much about Emory, but I am free to answer any questions you may have about UIUC as I was there for my master's.