Let me help you out with this BB. I have worked in BigCommerce, Shopify, Volusion, 3Dcart, MagentoGo as well as Yahoo small business and Godaddy as well as open source carts Presta Cart, CS Cart and Zen Cart. What you are talking about when you say "just check the box" means you are NOT using a fully responsive web design. That means you are using one set of code for desktops and tablets and another set of code for mobile and you are also using their cookie cutter code. When it is Fully Responsive, it means that you are using one set of code for any size screen. To check any website, minimize the screen in the top right and drag the right side of the browser to the smallest screen size (probably 330 px). If you see the entire website adjust as the screen shrinks, then it is fully responsive. If it stops adjusting at about 1000px then it is using multiple sets of code and is NOT responsive.
As for Worldofleggings.com, it has huge customization as do all of the Company's websites. If you right click and inspect the various elements, you see that they have used everything from customized Bootstrap, Ajax as well as Jquery. That customization is not built into basic cookie cutter templates that you are probably using. I also see that they have done a very good job making the sub code for all browsers as well as old versions, very nice. The UI is built very clean using both the latest versions of CSS3 and HTML5.
I can say that if you hit the button enabling the cookie cutter mobile mode in BigCommerce, you dont know much of anything about customization. Sorry bud, but thats just a fact not a cut down. UI coders are $60 - $100/hour skill sets and it would be very expensive if the Company outsourced all of this coding. Using Ajax and Jquery, as well as Webkits, is very complex and the Company's sites are very well customized, very clean and up to date, from what I can see from Inspect Element.
BTW, the underlying source code that drives the UI interfaces (CSS/HTML) is written in PHP which is complex code that is done by extreme and talented code geeks. If you are playing around in an open source cart, you had better know what you are doing and then some. If this Company is doing all of this customization inhouse, very very nice!
If you would like, you can tell your website url and I can give you some thoughts on your site. No biggie
