I have two Date Objects:
2017-01-13 11:40:17 +0000
2016-03-15 10:22:14 +0000
I need to compare
There's no standard type for a time-of-day. A reasonable type to start with is just a tuple:
typealias TimeOfDay = (hour: Int, minute: Int, second: Int)
To create these TimeOfDay values, you'll need a Calendar. By default, a Calendar uses the device's system-wide time zone. If you don't want that, set the Calendar's time zone explicitly. Example:
var calendar = Calendar.autoupdatingCurrent
calendar.timeZone = TimeZone(abbreviation: "UTC")!
Now you can use a DateFormatter to convert strings to Dates (if necessary), and then use calendar to extract the time-of-day components from the Dates:
let strings: [String] = ["2017-01-13 11:40:17 +0000", "2016-03-15 10:22:14 +0000"]
let parser = DateFormatter()
parser.dateFormat = "yyyy-MM-dd HH:mm:ss Z"
let timesOfDay: [TimeOfDay] = strings.map({ (string) -> TimeOfDay in
    let components = calendar.dateComponents([.hour, .minute, .second], from: parser.date(from: string)!)
    return (hour: components.hour!, minute: components.minute!, second: components.second!)
})
Swift.print(timesOfDay)
// Output: [(11, 40, 17), (10, 22, 14)]
Finally, you can compare these TimeOfDay values. Swift comes with standard comparison operators for tuples whose elements are Comparable, so this TimeOfDay type qualifies. You can just say this:
if timesOfDay[0] < timesOfDay[1] {
    Swift.print("date[0] comes first")
} else if timesOfDay[0] == timesOfDay[1] {
    Swift.print("times are equal")
} else {
    Swift.print("date[1] comes first")
}