The only reason Picard got in that situation is because he stopped his attack. Initially, they pounded the Borg ship pretty easily. It was only after he stopped to investigate the cube, giving them a chance to adapt and repair the vessel, that the E-D weapons were ineffective.In Tng the first borg encounter, Picard and his ship (which was way beyond anything in tos era) couldn't take down one cube, hell he came close causing the assimilation of his whole crew.
In an initial encounter, if Kirk keeps up the attack, the Enterprise should win. A second fight though, that'd require the old anti-computer Kirk fu.