Calendar apps for iPhone are a tough thing to advise for because different people use them in different ways. Some people are busier than others (meeting wise), and others use their calendar as a to-do system (personally I question your sanity if you are this way). All of the primary calendar apps I tried are great but might not fit how you use a calendar app.
When using third-party iOS apps, it’s straightforward to try new ones because they request access to your calendar data using Apple’s APIs (so it works with Exchange, iCloud, Yahoo, AOL, and Outlook.com). This feature keeps you from having to set up different apps individually. I’ll explain what I like about each one, and which one I like best.