This is a great, detailed piece of work, and a real contribution. I think an interesting challenge to comparing these programs is that in-kind food transfer programs tend to have one central goal: Improve food security. Cash transfer programs, on the other hand, tend to have a broad range of goals: Improve food security, improve school enrollment (or attendance, or both), improve health investments (beyond nutrition), etc.
My intuition (not backed up by specific evidence) is that cash transfers would be better for achieving these other goals, simply because cash is more fungible. I actually think that's what's behind the idea that "cash is a first-best option": Not that cash is better at achieving food security, but that cash is better at letting the poor achieve whatever it is they need to achieve.
Does your paper or the papers you examined look at other outcomes (e.g., education, health), and is there a tendency in the findings?