Which eCommerce application should I use or which framework to use for building eCommerce application?
Same question as with frameworks, CMSes and similar open source solutions comes as well with which eCommerce PHP application to use.
There are quite a lot of existing open source very good solutions for eCommerce purposes currently available in PHP. Choosing the right one for the project or a right PHP framework for eCommerce depends on your knowledge and project specifics.
Some of popular eCommerce solutions: