Calendar App (built-in iOS app)
Displays day, month or year views. You can enable a timeline view to go along with the calendar. There is no week view. The month view doesn't display daily event details unless you click on each day. The Today widget only displays the current day's events. Overall, I would prefer to have the flexibility to view details at a weekly or monthly level.
Fantastical 2 by Flexibits Inc ($3.99)
I decided to try this app because it was highly rated and recommended. It also supported URL schemes which were big before sharesheets. Fantastical has a unique timeline view. There is a continuous vertical scroll of events with days scrolling sideways like ticker tape. That's pretty neat. There is also a month view if you pull down on the ticker. You still have to scroll through the days in this view. There are no traditional calendar views by day, week or month and there is no at a glance view of events that week with full details. The widget offers a month view with a timeline under it. The app supports natural language input when creating events. E.g. You can type "Lunch with Bob at noon tomorrow" and it will enter in the relevant date/time and title. There is also a unique keyboard for selecting the time of the event. It allows for multiple alerts and supports Launch Centre Pro and TextExpander. I probably used this app for a year or two before I got tired of having to scroll through events. I was looking for something a little more traditional yet customizable.
My Recommendation: Week Calendar by WeekCal B.V. ($2.79)
I heard about this app from a podcast. The general consensus was that it could look a little messy but it had the most features and views. I purchased it and it is feature rich. It did not disappoint. It has many views - List view, day, agenda (laid out like a planner), week, mini month (event titles shown), month and year. It allows for a ton of customization from conditional formatting (e.g. event contains "meeting", colour it yellow) to customizing how it talks with other apps to allowing pinch to zoom in/out in a view to editing inline without opening the event. The Today widget shows a timeline view of today and tomorrow. I can't state how happy I am with this app. It satisfies all of my needs in a calendaring app. It is worth the money in my opinion!
myCal PRO: Calendar & Event Organizer by johnhair.com ($5.49)
This one has a detailed month view, good week and day views. There's a cool watermark feature showing which events belong to which calendar. You can customize the font sizes to display more on the screen. There is no today widget though. Overall, a decent effort.
Easy Calendar by T. van Zummeren ($2.79)
This one focuses on the Agenda view exclusively. It has a simple interface, night mode, font size adjustment options and a few other features. It uses popups to view days and appointment details. This app has no Today widget. It's decent, easy to use and configure but I need more.
Calendars 5 by Readdle ($9.99)
This app has a number of views including a timeline, day, week and month view. The month view shows details for all days that month but you can't scroll if days have a lot of events. You can set up as many reminders as you want. It also supports Tasks which is unique for a calendar app. It's other distinguishing feature is natural language input like Fantastical. The Today widget is fairly basic, showing only today's events.
Calendar Widget Apps
Week Cal Widget for iOS calendar by Crater Tech LLC ($2.79)
Displays week view in a widget including event details. Good for an at a glance view but events with longer titles may get truncated. You can increase the height of the widget to help but you can't view the full event without opening it. Decent for a widget.
Agenda: Widget+ by Jeeeyul Lee ($1.39)
Displays in a timeline view. Has a number of customization options related to adjusting formatting and spacing, and seeing how far an event is from your location. This widget displays today and tomorrow.