Tyyrlym is quite correct, neons are not forgiving when it comes to their environment. All the sources I have found say they prefer a slightly cooler temp than most aquaria (20-26C in their native waters) and a pH below 7, and this even though all neons are now commercially bred and not wild caught (unless you are particularly fortunate to find wild neons). You cannot alter what's in their genes. They are also intolerant of any changes so if introduced to a well established aquarium having suitable water would probably settle in better.
Cardinals until recently have been all wild caught, but tank-raised fish are being seen now although the wild fish are still prevalent (at least in my area). Cardinals will be fine in warmer temperatures (they are often suggested for Discus
tanks) but are perhaps more intolerant of conditions like pH due to the fact that they are found in waters with a pH of 3.5 to 5.5. Some argue they can adapt to hard water, but I wouldn't risk it. Harder water causes calcium buildup that blocks the kidney tubes. The fish from Columbia are a little more hardy (don't take this too literally) than the strain from Brazil which in my view is more beautiful; I have both in my 90g, the Brazilians are wild and the Columbian are a mix of wild and tank-raised.
The third "neon" sometimes available is the false neon or green neon, Paracheirodon simulans
. It comes from very similar waters as the cardinal (in somne areas they are found together) and is intolerant of water above pH 6.6 and like the cardinal can be happy in warmer aquaria. Both these fish will not thrive in changing water parameters or "new" tank setups. There is now a fourth "neon" discoverd by Heiko Bleher in 2007, but he says it will be years before it is widely available as it is very difficult to get to the area. You can read about it and see photos in the October 2008 TFH.