The winner will be the captain with the least competent engineering staff in charge of shields and weapons.
The reliability of any system in the Trek universe is inversely proportional to the competence of the people available to fix it. The only exception is the holodeck-- no one knew how to fix it, but it kept failing, anyways.
Scotty could rebuild a transporter in his sleep and Geordie could work miracles with a warp core, or why when both of them were on the Enterprise in "Relics", some excuse had to be made to get them to a ship that was already without fully functional warp engines and transporters.
Kirk, in the Enterprise, is hosed, because he does not have any of the unspecified technowizardry that reduced combat ranges by a factor of a thousand in ST:TNG (note: this was really due to the inability of ST:TOS to present multiple ships in the shot; unless, they were in close formation, so all ranges were cleverly written to prevent two fighting ships appearing in one shot). The Enterprise D can engage an unmodified Enterprise at ranges of tens of thousands of kilometers, but is effectively cloaked to return fire at all but the shortest range.
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