If you want truly authentic French food, you will probably enjoy Bistro. Chefs I think has yummy food as well, just not as fancy. The atmosphere at Chefs is really fun and boisterous (which we love). We ate at Bistro once and were unfortunately seated next to a couple with their 1 and 2 year old (screaming loud) children. Not very romantic. Just got unlucky I guess.
Chefs and Bistro are two completely different dining experiences. Chefs is more of a French brasserie - busy and a bit louder, with informal dishes. Bistro is fine dining, with a more hushed setting and more 'elaborate' dishes.
Why not check out both menus at Allearsnet.com and see which appeals to your party more?
Personally I'd go with Bistro every time but I do really enjoy Chefs as well, and we go for lunch there every other trip or so. When we took my family to WDW for two weeks in 2006 Chefs was their favourite meal of the entire vacation!
Edited to add: We have thankfully never had screaming children at Bistro when we have been there, and I must say I don't really think it's a suitable venue for toddlers. The sizes of the dishes are designed for appetiser > entree > dessert, so a meal is likely to take longer than at Chefs. I imagine most kids are bored by the time the entrees arrive...
We like Chefs for dinner because it reminds us of sidewalk places in Paris. Its loud and rushed but good food. You can get in and out. We like Bistro so much for dinner. It does take much longer, the food is more elegant, the atmosphere is different and the views of the fireworks are great if you get a window table. I don't think its fair to take a toddler there without toys and other forms of amusement.
As others have said, those are completely different dining experiences. I would pick Bistro, if I were not on the DDP and the menu prices seemed acceptable.
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