With the new changes to Platinum rate as of Dec 19 2014, this article no longer applies. Upgrading Ancient Dragons is now a decent option as upgrading will give similar increase as getting a new dragon.
If you want to increase your Platinum rate as fast as possible, consider the increase in rate you get from each type of upgrade/summon.
Upgrading Guardangel will give you +1 Platinum per hour. Getting Gorgoneia will give you +9 Platinum per hour. Gorgoneia Since their costs are close to the same, definitely get Gorgoneia first! It will pay off fast!
Piercing dragon does cost more since you need to open up the Sapphire Mine. But still is a better investment than upgrading the other dragons.