Depending on what wheels you use, a circular base may/may not be moved around more than a rectangular base. In general, I'd think that a rectangular base would be more sturdy, but that could just be an opinion. However, welding and cutting a circular base would surely provide a significant problem, unless you are associated with a metal fabrication shop. But other than that, there's really not much difference (that I can see). A circular design or two would certainly add some variety to the competition.
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