Hi OP!
We've been to both Tutto and Chef's multiple times, and we prefer Chef's. The food is very good at both, but we would recommend Chef's for several reasons. (OP, I'm not sure if you are traveling with children, but I'll share our experiences in case they are helpful to you!)
First, we enjoy several child-friendly Italian restaurants at home, but it's not as easy to find a child-friendly French restaurant! So we like to take advantage of the opportunity to enjoy Chef's with our kids at WDW. We also prefer the atmosphere at Chef's. The windows are large and the interior is light and bright. We've experienced consistently great service at Chef's, and the CMs at Tutto have not been as warm or welcoming towards our children. (When dining at Tutto as an adult before kids, I thought the service was much better.) Finally, one of our three boys is quite a picky eater, and he absolutely loves the mini burgers on the children's menu at Chef's!
We make ADRs for lunch on arrival day for Chef's so that we can meet Remy right away - it's become a new tradition, and so much fun! The CMs handling Remy have been outstanding - so enthusiastic and animated. Each time, Remy spends quite a long time at our table with our boys. They are so excited to see him, and we never feel rushed. We love it!
Good luck with your decision, and have a great trip!
