At this point, Janeway knows next to nothing about the Borg. Not unlike Picard, who had much more on-hand experience with them. Sure, by the end of the series it was the other way around, but at the time of Scorpion... no. Picard would know better then to trust the Borg, and would never even consider an alliance. He would find other ways to get to the core of the problem, perhaps even open up a dialogue with 8472.
I wonder if Janeway, knowing what she learned of the Borg by the end of the series, would be so open to the idea of an alliance with the Borg.
How do you open up a dialogue with a race whose goal is to destroy everything in your galaxy. The only way that one was established was because Voyager and the Borg discovered how to defeat the bioships of Species 8472. So 8472 had a reason to be pissed. Sure, they overreacted a bit, but still.
Did Janeway even try to establish contact with 8472? I think she only reasoned that way because Kes told her that 8472 were having so many nasty thoughts. I don't remember any attempts of 'opening hailing frequencies'.
Picard has always been the better diplomat between those two. He would try to find another way around this situation then allying himself with the Borg.
Picard is not stupid, and he may have been hurt nearly beyond repair, but he knew how to compartmentalize his feelings.
1. Species 8472 is out to destroy all life in the galaxy.
2. Find a way to stop them.
3. Our idea will only work with Borg help.
4. Ally with the Borg.
5. Deal with Species 8472.
6. Cut and run from the Borg.
It was later found that 8472 only wanted to destroy everything here AFTER the Borg violated their space. The Borg were the first to act in that little war. Sure, 8472 overreacted a bit with their 'destroy everything' attitude, but the Borg instigated it all.
As far as I can remember, Janeway never even tried to establish contact with 8472. Kes told her that she picked up all these nasty thoughts, and Janeway acted on that. When they realized the Borg were the once that started it all, it was already to late.
Picard has always been the better diplomat, and would not choose a side so easily, not even if the Borg were involved. He would find out what compelled the other side aswell.