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It wouldn't make sense for the PlayStation 4 to be released on December 13th. They will release it a month or two before December so it is available the entire Christmas shopping season. If Sony released it that late it would kill their sales because most people would have already bought the new Xbox console and would not bother with the PlayStation 4.
Hmm, while anything is possible, I'm definitely sure that this won't be the actual release date of the PS4. The reasosn for that is simple, it's pretty obvious that Sony will want to release the system before the biggest shopping day of the year, which is Black Friday. Black Friday is on November 29th, so I expect the PS4 to be released a couple of days eariler, like the 27th.
As I have already mentioned in another thread PS4 is outstripping Xbox One by a huge margin in all over Europe except for UK, where they are ahead by 2:1. They are cruising now leaving Xbone way behind in terms of pre-orders. So, I don't think that an earlier release date has helped Microsoft so far.