Well I would have liked to have seen Riker dealing with the borg on the enterprise, considering his history with them in BOBW. I agree Picard's flipping out scene would have been better if he was screaming at Riker.
If I remember correctly, the initial plan was for Riker to be aboard the Enterprise
battling the Borg while Picard would have been on the surface interacting with Cochrane. Then someone among Berman, Braga, and Moore realized that, given Picard's personal history with the Borg, he needed to be aboard the ship, so the Riker and Picard roles were essentially reversed.
Frankly, I have a hard time imagining that Patrick Stewart would have been happy with the script had Picard been part of the fish-out-of-water comedy storyline.