At least for stills there's simply no way the iPhone is faster, burst mode apps or not. (I speak as a frequent user of both DSLRs and iphones.) The ability to zoom and crop means you can get shots with a DSLR than an iPhone could almost never get (barring ungainly tricks like shooting through binoculars) and you can't freeze action.

An iPhone is never faster than a pro DSLR. From hip to eye, power on and shooting in under a second. There's a reason the power switch is part of the shutter.

Nooope, it's not even close--the iPhone is slow, inflexible, and poor-performing compared to a pro DSLR hooked to a 24-70 f/2.8 or 70-200 f/2.8 zoom. Consumer DSLRs are kind of pokey, but the pro models go from "off" to "shoot" in a fraction of a second, with no perceptible delay between hitting the shutter button and an exposure. There is no faffing about with P mode or the like (only someone who doesn't know how to use his camera would be caught out doing this).

The iPhone does have an advantage in network connectivity, but it's comparatively unlikely to capture the couple of moments worth saving.