Before you go lunging after the available bench option, think through what kind of storage you want under the lathe. Personally, I find shelves behind doors almost useless. You have to squat down, stuff gets buried in the back, the lighting sucks, etc. I much prefer drawer storage as you can see in the stand that I built for my 1340GT. Many others buy a tool storage box and adapt it into the stand. There are plenty of examples here on H-M using this strategy. From a value standpoint, the Harbor Freight tool boxes are very well made considering their low cost. Most systems that
do not have a flip-up top lid are either too tall to fit under the lathe without some modification (removing the casters) and/or elevating the lathe to a height that may be objectionable. The top-box alternatives are more practical, but you'll need to modify the box to remove the flip-up lid and come up with another drawer-slide mechanism to use the space such as the following example:
Both of the options you mention would be serviceable as a platform for the 1340GT. That said, I prefer the blue one you show in the photo - it's more rigid and more easily moved around with a pallet jack. If you get the HD version, I would encourage you to think of adding some crossbars on the legs to act as stability gussets.
You didn't mention the height which might influence your decision based on where you want the lathe positioned given your height, and what you plan to put under the lathe. Here is a link to a simplified drawing that will give you more details on working height considerations - this is part of the drawing package for the stand I built