I have a few Neons and about more than double the amount of Cardinals in the same tank... it's quite funny because they all shoal together as if they were the same exact species and not just closely related cousins. My centerpiece fish are a pair of GBR's. So far, they all get along fairly well and are looking pretty healthy. That's pretty darn good taking into consideration that my tap water is pretty hard in AZ.
I'm not sure if you have a Petsmart in your area or if you're against chain pet stores (like some of the hardcore aquarists are), but if you're willing to stray away from the LFS for a bit (in which SOME cases I am), they have tetras (including cardinals and neons) on sale for a $1 each. I believe the sale ends on the July 24th or something... and no, I DO NOT work for them! I am slightly biased towards them because I DO LIKE that they have a 14 day fish guarantee policy which gives me peace of mind being that these particular tetras are so darn sensitive...
Anyway, IMHO, assuming that your tank is cycled, if you have a good filter rated for a larger tank over the 20 gallons you have, and you keep up with the PWC, you can keep a whole lot of the tetras and a center-piece fish easily. I'll even go as far to say that the 10 & 10 as you originally inquired about would work. However, I'm sure you already know this but Neons & Cardinals are super sensitive to water parameters so you should slowly introduce them to your tank, and not all at once. You should not only temperature acclimate them but also use the "drip method" so that they aren't shocked by sudden changes to the pH, hardness, and numerous other water parameters. Moreover, you don't want to overload your bio-filter and it would be wise to allow the beneficial bacteria to multiply and compensate for the extra waste. Then again, if you're eager to stock your tank, as I mentioned before, you'll have to step up with more frequent PWC's to keep the ammonia levels down until your bacteria levels can catch up.
All the recommendations that a lot of people like to give are based on assumptions derived from guidelines, such as that semi-dumb stocking guide. However, not all are bad and there are some really good advice out there. Some would argue that I'm giving bad advice, but I don't care. The point I'm trying to say is that there are some exceptions to the rule so you just have to understand (with research and experience) when you'll have to step it up in certain areas (i.e. filter, pwc's, etc.) if you want to push the boundaries of stocking. Case-in-point, I've done it without "excessively" overstocking, and tastefully so with success.