The big distinction between the two of them is that donations to a 501(c)(3) charity are tax deductible and therefore may not be used to unduly advantage any commercial entity, while donations to a 501(c)(6) are not tax deductible and thus are unrestricted.
If it's a 501(c)(6), then the foundation will serve its biggest donors first and foremost. In theory, it may also serve the public good — but only to the extent that it is in the interest of those donors.