Cloud based web stores: is like having an apartment in a building and sharing resources. You can make some changes in your suite (theme), but are governed by the programming restrictions or access, that can prevent you from adding in custom functionality or 3rd party content that you might need as you evolve your business. Many common add on functionality needs are addressed through 'apps/plugins' made available, however they may or may not work on the platform you subscribe to. It is the platform you subscribe to that dictates and limits all of what that web store looks and navigates like.
"Very cost effective to get into as you generally choose a web store themes, update colors, update your logo and you're up and running."
Self-Hosted web stores: is like having a home on your own lot (self-hosted) that you can alter both inside and out and expand (scalable) with no programming restrictions. Fully customized design and programming capabilities makes this option an excellent solution for companies that are more focused on their online presence and have a list of ideas and ambitions that will constantly be evolving. Self-hosted web stores are generally faster to browse, far more self administratively advanced and can address many complex eCommerce ordering requirements such as streamline fulfillment for shipping and just in time order, feeding multiple web stores, wholesale b2b tier level pricing and custom reporting.
"More expensive to customize and support, takes more time to develop, but you get 'exactly' what you want and need, in every aspect."
Summary: About 85% of eCommerce retailers fit the 'Cloud hosted' theme and 15% 'Self-Hosted'.