On FMP/FMP Advanced, I can set any field to have the Date Picker control style, and it will automatically show the drop-down calendar when I click into it.
On FM Go, it will show the Date Picker if and only if the field is set to Date format, even if the Control Style is set to Edit Box and not Drop Down Calendar.
I discovered this because I had a global field that I was using as a search parameter and I decided I wanted three fields, one of which was to search for a date, so I just copied the first field twice in Manage>Database and I decided to make one of them a date field in my layout. It works fine on FMP/FMPA, but when I tried to use it on the iPad the date picker wasn't coming up. It took me a while to realize that the date picker would only appear if the field itself was set to Date format.
I feel like if I set the Control Style to calendar (especially if I choose to show the icon for the calendar), FM Go should show the Date Picker regardless of the format of the field, and the fact that it doesn't is a product issue.