I have certainly seen cardinals and neons shoal together, but in the end, there's so little difference that having a mixed group provides you no benefit other than being able to say that you've had both. At a glance, they look essentially the same, with cardinals being slightly more colourful.
Everything else being equal, I'd say go with the cardinals. They're typically a little more expensive, so if budget is a concern, I'd go with the neons. Either way, there's not much point in getting both.
Also, when stocking, consider stratum. Some fish prefer the top, some the middle, and some the bottom (others don't care). Most of your fish are top and middle dwellers. You'll see Charlie and sky suggested corys and loaches. These are both bottom dwellers, and you'll appreciate their assistance in keeping the tank tidy.