Range boxes vary greatly in size, configuration and capacity. I have an old Pachmayr box which I used for PPC.
To get to the inquiry, here is what I carry in it. I have enough tools, in a flat steel box, to take down any of my firearms as far as I would want to under field conditions. Some of these are specialized tools. Others are general tools for which I have a specific use (such as a 3/4" 12 pt socket for removing the bushing on my S&W 52). I am well past PPC now, so this tool kit has actually expanded to cover any firearm I may take out. I also carry two holsters that will accommodate my PPC revolvers (thus anything else, given their size), accompanying belt, speed loaders, speed loader holder, loading plates, sight blackener (spray and carbide torch), rosin bag, target pasters, ear protection. I have removed the tray which holds handguns upright in brackets. I keep my handguns in individual zip pouches. I can stack these on their sides on top of the flat tool box, which is much more efficient and affords more protection to the handguns. Ammo is carried separately since I use military surplus ammo boxes, always have. I don't carry a first aid kit (have that in each vehicle), nor any sort of snivel kit.
All of this is a lot of weight and bulk. But this box carries too many memories to ever give it up. My bride gave it to me right after we were married. Now, besides the scars from use, it is covered on the outside with decals and patches from my competition years, and on the inside of the lid, possible pins from the PPC matches, plus a spotting scope. In the thread in the Lounge on bullseye shooting, several shooters have gone from such boxes to range bags. Probably more practical since you can tailor the bag to accommodate only that which you decide to carry. That is what I do with camera bags.
In watching some of the cowboy action matches on the tele, it appears that (at least) a fair number of competitors use hand carts to transport all the necessary gear from their vehicles.
One warning, an immutable law of physics: Stuff expands to exceed the space allotted for it.