Since you already have the Montaigne go for the Chanel. I think that the big size makes it a casual bag.
I think it depends what you mean casual style. Jeans and a sweater/t-Shirt or full on outdoor clothing?
I love both Chanel and LV but I’m going with the Maxi as my vote. You already have a Montaigne so go for a different bag. I think all the classic flaps can be dressed down or up. I’ve worn my medium CFs with suits and with jeans. As others have stated the Maxi will be more casual looking based on its size.
The Maxi will probably be heavier than the Montaigne, so that's something to keep in mind. If you already have the Montaigne, then go for the Maxi. I wear my jumbo with any outfit so I think a maxi will be fine as a casual bag.