The DDG1000 is definitely not your father's destroyer, no matter who your father was. The ship is a floating testbed for all kinds of interesting stuff. I had a very little bit to do with some of the stuff aboard her, so am more than slightly interested to see what succeeds and what doesn't. The most interesting stuff is deep under the skin, and the generalities of it are public information. You know it's an interesting design: the project has been going on for a very long time and has nearly been canceled at least four time that I know of. But the Navy's right on this one - you don't win the next war with the last war's technology, and the Navy hasn't rolled anything really new out since the first generation of the Aegis suite.
Her shape is optimized for low radar return from all angles while not impeding operational effectiveness. She's a logical follow-on to the Littoral Combat Ships the Navy has been building over the last decade - a blue-water ship with baked-in stealth, DDG force projection capabilities, modern power, sensor and control technologies.
The answer to Another Ahab's question is: it's what the Navy says it is. Just like the Japanese navy says their new 'destroyer' is a destroyer, even though it looks a whole lot like an assault carrier. Our 'destroyers' have really been frigates since at least the Arleigh Burke class came out, if not before - they're big and powerful enough to be effective single combatants and are capable of extended independent operation, which has been the traditional difference between a frigate and a smaller post ship going all the way back to wooden ships with sails and blackpowder guns.
Another proof that our destroyers really are frigates: they do frigate jobs. Destroyers haven't historically been used for the kind of work that the Arleigh Burkes generally do after the end of the cold war. If you're not planning on going to war with another massed fleet or landing divisions of troops under fire, you don't need a massed fleet full of specialized vessels. But you generally do need ships capable of showing the flag and doing/supporting small unit operations. The DDGs have grown into that general purpose ship - they can act as cold-war-style defensive pickets for a carrier battle group or (more commonly) run around alone or in small groups and do whatever needs to be done.