Apple is not stricter. There is a lot said and written about Apple, and to be more exact, iBooks restrictions.
Epubcheck is fun, but rather useless. The messages are not usable if there are messages at all.
You're better off using FlightCrew by Valloric as your validation tool. It does way more and better checks and, as a bonus, gives a much better description about what is wrong with your ePub.
Please run it through FlightCrew and report the errors you cannot solve. We will help you if we can.
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