Right. That’s why I specified in my OP that Neo had all his Matrix powers and Murdock has all his tuning powers.
Except that Neo does have powers outside of the Matrix in the second and third movies, making your comment totally irrelevant.
Except that Neo’s powers outside the Matrix couldn’t actually do anything to affect Murdoch’s tuning, because Murdoch isn’t a machine. Thus making … yadda yadda, let’s stop there before we take it to the Pit.
I’d argue that Neo was never able to fully determine his real world powers, thus making the result of any “real world” battle between the two unknowable. 
I’m going to bet on Mr. Murdock, yes.
Not so much because of any analysis of power-level versus power-level–in sheer wattage in his milieu, Neo might well have more.
The deciding factor is comparing how quick each is on the uptake. Neo…isn’t. He looks bovinely placid in the face of relentless, glacially paced exposition over the course of three ballooning movie lengths. John Murdock, on the other hand? He doesn’t have time for that; he starts getting exposition, and he properly cuts it off. This comes from being simply naturally brighter–hey, life’s unfair.
It would play out something like this.
Neo: Whoa. Where am I? Last thing I knew, all the flying squids in Machine City were forming a giant airborne billboard that said CHRIST FIGURE with an arrow pointing at me.
Morpheus: <strolling around with his arms crossed behind his back> Neo. Welcome. To the real world. <proceeds to deliver twenty seconds’ worth of information (to wit: “that dude over there, the guy who can act? Kick his ass, quick!”) but spreading it out over ten minutes, not counting a side trip into a virtual dojo, and making sure to book reservations for a fifty minute visit to the Oracle so that she can deliver the same ten seconds’ worth of information (“You have to kick that dude’s ass. Here, have this cookie.”) slightly faster than Morpheus can.>
Neo: <chews cud placidly>
John Murdock: <looking thoughtful because he’s working on getting an actual park zoned into the place, looks up irritated as Dr. Schreber taps him on the shoulder cringingly.> What?
Doc Schreber: John. That man. Is dangerous. You must…trustme, John.
John Murdock: That guy over there in trenchcoat?
Doc Schreber: Yes. He knows. Kungfu and can…fly.
Morpheus: <tortuously explaining the Allegory of the Cave, using Legos>
Neo: <placidly chewing cud>
John: <scowls. Two buildings slam together, reducing M&N to paste before the camera can get through the first 180 degrees of its slow-mo spin. Then he goes back to psychically generating greenery.>
Oddly enough, this describes every person in Dark City and 80% of the people in The Matrix.
Good point.
Script changed in pre-production to:
John Murdock: The skinny pale guy in the trenchoat who’s not wearing a hat?