Their relationship, such as it might have been, was another lever to be exploited by any who had the means. No doubt that when it came to the hard choices, each of them played the other and used their relationship to own advantage.
Certainly LP will have said pretty much what PS would have said, as far as informing on the other, but only one could make the better deal and that would come at the direct expense of the other.
What seems to have played out is that PS was put on public stage to do what he would predictably do (while constrained by FBI instructions). He was pushed forward to look like a fool while LS was dubbed "the lovely Lisa Page" and was kept out of the public eye while giving her testimony. This protected her from she would have done, predictably, under questioning.
Neither would have presented their case in a better light, but LS did her performance behind closed doors and (subject to less constraint from the FBI) presented what would be described, publicly, as more "forthcoming".
The deal was who would be center stage and who would be backstage. PS got to speak first, publicly, so that LS could be portrayed as reasonable by comparison.
One Anon's theory, anyway.
Cheers all.