Is my function nondeterministic one
I'm not sure if there is a flag, but there is a reference available at http://msdn.microsoft.com/en-us/library/ms178091.aspx of which built in functions are deterministic.

GETDATE() and GETUTCDATE() are nondeterministic because if you call them multiple times with the same parameters, which in this case are none, you get different values. In other words, the return value is not determined by input.

As far as why the second is slower than the first, check for implicit conversion between SubmitDate = @SubmitDate. Are they both datetime?