From the same page:
On the other hand, if you want one solution for all your date needs, don't need peak speed, or are trying to do more exotic date operations, Date::Manip is for you. Operations on things like business dates, foreign language dates, holidays and other recurring events, etc. are available more-or-less exclusively in Date::Manip.
This is the reason I recommend it, the speed is rarely a factor (for what I do, YMMV). The API that I use in 99% of cases is 2-3 functions.
Also AFAICS if you have a "Date and time" as a string there is no DateTime constructor to pass it to Date::Manip::ParseDate "just works". Getting a readable version of the data out also seems much harder than calling Date::Manip::UnixDate too.
But all of this just proves my other point, if you want an answer to the question "Which module should I use to do X" you can't easily get an answer ... you have to either pick a module and hope, or hack some code in directly that you know/think solves your problem.
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James Antill