ST:
There is really nothing wrong with the Browning. It is what it is: a modern single shot action that looks more or less like a Winchester 1885.
Whilst I have never had a Uberti apart, I have handled one and they seem to be pretty nice actions. Near as I can tell it uses the basic Winchester design, with some minor changes I don't entirely understand. I think the action would build up into a good Schuetzen rifle. Then again, if you were looking at a new barrel and stock, you might be better served selling the rifle and buying an original action. For better or worse, we all like the origninals.
Glenn