I thought about this one for awhile, and I struggled to figure out a winner for a long while. However I was reading some old Punisher issues the other day (handy) and G.W. Bridge, former agent of S.H.I.E.L.D. made a very good point; the only reason that Punisher was allowed to run around for so long and not be apprehended (by the police and S.H.I.E.L.D.) was because they willed it so. The authorities kinda like the Punisher because he gets the job done that they can't lawfully do. With that thrown out of the window, we've got Nick Fury ready to bring the Punisher in.
The battle itself will be a fierce one with evasive manoeuvres and explosions of violence left right and centre. Both men are relentless and when they're in that zone they can be unstoppable. With an extreme pain threshold, neither is going to succumb to the actions of the other for a long time, but I think this comes down to who has more bullets and simply put, that's Nick Fury. The Punisher has enough supplies to last a long time, but he doesn't have a near endless supply like Fury whose knowledge of S.H.I.E.L.D. tactical basis is second to none. He knows where to get what he needs to survive and I think that will be how he conquers the Punisher.