The main failure is in the high end bright spots, the highlight roll-off does not look like nature. Nature is the goal (not film). Film happens to mimic nature better than any digital sensor ever created because of its analogue characteristics. This is no trivial matter.
It's not a matter of digital vs. analog since every digital camera uses an analog sensor...there is no such thing as a purely digital sensor (ever heard the term AD conversion in digital cameras? It stands for Analog to Digital...the point at which it happens is a key difference between CCD and CMOS sensors). But yes, highlights are classically a difference between film and digital.
Nit picking aside, I asked for specific examples (I'm particularly interested in examples from the POTC4 trailer as compared with samples from the original films). Because nothing you've brought up is new to the table, and a lot of very smart and talented people have been working with issues like highlight roll-off. All you can really come up with is some ethereal magical non-description without really illustrating the difference. I have a hard time believing it's as clear cut as you make it out when we're an age of extreme digital color grading regardless of capture technology.