I have the CED range bag which if I'm not mistaken is the same as the shooter's connection or very similar. I used the CED range bag with Dillon boarder shift ammo bag it fit nicely in the compartment of the CED bag. I pretty kept everything essential in the Dillon bag that i would use on a stage such as extra mags, mag brush, ammo etc. and just leave my range bag with extra guns/parts in my truck. I used this set up for about 6 years until I picked up a medium Double Alpha backpack off of a prize table. The back pack IMO is the way to go. The only draw back of the back pack is if you shoot production or SS you might have a problem with the back pack hitting some of your mags if you don't take the mags off your belt when walking between stages.
Also, IMO some type of cart whether it is wagon, 3 gun buggy or jogging stroller is a must have if you're going to be lugging around full range bag unless you shoot at very compact range.