There is one cart system that is far more popular than all the rest, in fact, 1 out of every 4 new online stores are built on the most popular shopping cart, Magento. Even though it is a relative newcomer, as compared to the previous favorite, it has quickly risen to become the most popular cart used by businesses today.
Back in 2011, the developer, Varien (now Magento, Inc.) was purchased by eBay, and its popularity has continued to soar. There is both a commercial version, a paid hosted version, as well as a “free” open source community version. It is to eCommerce what WordPress is to blogging, the stand out “leader of the pack”.
Since nobody directly answered your question about “leaders in the pack”, I will try to help you out with the answer to that.
I must disagree with your assertion that “not something you can run on shared hosting”. Magento will run well on shared hosting provided you select a host the specializes in hosting Magento stores and you configure and optimize your store.
It’s true if you go for a budget hosting company that tries to put a couple of thousand websites on a single server, then you will probably have a problem unless you have a small store with little traffic.