Yes, a group of either should be fine. The neons must have cooler water, as do the cories, while the gourami is a tad warmer, and the cardinals can manage that with no problem. A range of 76-77F would be the upper limit for the neons, and the lower limit for the gourami. The cories will be fine. I would not go warmer, even with cardinals instead of neons, because of the cories.
As for hardiness, the cardinal is probably better these days. Neons have been inbred for decades and they are now showing weakness and susceptibility to almost anything. Cardinals at least in NA are largely still wild caught, or if commercially raised it has not been too long yet.