I think it's been an accepted fallacy here that Hart was the best goalie in the world outside of Neuer. But outside City, many have never shared this view. Like I've often said, Hart is a good goalie. One of about 10 very good goalies in the Prem. Bravo I believe is a better goalie period. Even if you ignored footskills and ability to play from the back.
On the following factors
Positioning, Reflexes, hands, Area control, shot stopping, diving and limiting errors. Bravo is probably better in most of those area. And when you add sweeper/keeper qualities to the mix the gap increases exponentially.
The fallacy here is most are pretending Bravo is simply just better with his feet, but overall inferior to Hart what has been deemed in England to be the traditional qualities of a goalkeeper. Exclude continental qualities and judge them simply on the traditional stuff and Bravo is still a better goalie. I know many of us believe Joe is going to Everton, but for my money, I don't see how he beats out Steklenburg. Who is a solid goalkeeper in his own right.
As for your question who would Stoke want? Perhaps Joe, coz he is English. And frankly I agree that if you have a good English goalie, don't go wasting Foreign slots on that position. But if you simply are asking who is better? It's probably Bravo everyday of the week. But that's not the only question team's ask when they are making these decisions.