I am wondering if there is a downside to using multiple mail and calendar apps on my iOS device? Specifically the iOS devices come with apple provide apps for both, but I have found 3rd party apps that work better for me. If I have both (Apple's app as well as the 3rd party app) configured, am I doubling the amount of data & memory I am using on the iOS device?
Yes, you definitely will double the data sent, if one uses two apps for the same account.
However, using different programs may be useful. For example, if you want to separate your professional Exchange E-mail from your personal accounts. This way, there is a logical separation, and you run less risk of accidentally sending out a personal mail on a business acount, and vice versa. Some mail apps even have password or PIN protection (for example, Divide), which will keep your E-mail accounts safe, even if someone swipes your phone when you are using it.
If you use two mail apps for the same account you will be downloading the same information from the mail server twice. Which will result in around double data traffic. Emails isn't usually so much data per email but that depends of course on what you receive and how many emails that is going to be downloaded.
If you want you can check how much data that your email app used under Usage in iOS settings.