I will take a wild guess and say it might be the same bag, only one is the leather version and one is the signature fabric version of the same style.
Sometimes that is how Coach differentiates one from the other with a one or two digit numerical difference.
Example, leather Leigh #11128
Signature fabric Leigh #11141
Thanks! I think you're right, I just read a few of the listings more carefully and noticed that the 11349 is fabric
The 350's shape is mosre angled than the 349.