AWS Public IP to AWS Public IP Traffic

The traffic will stay on the AWS network, see below from the VPC FAQ

Q. Does traffic go over the internet when two instances communicate using public IP addresses, or when instances communicate with a public AWS service endpoint?

No. When using public IP addresses, all communication between instances and services hosted in AWS use AWS's private network. Packets that originate from the AWS network with a destination on the AWS network stay on the AWS global network, except traffic to or from AWS China Regions.