What we know:
1.) The stargate and DHD we see on the vessel Destiny is among the oldest of the stargate designs. (for reference, see this Gateworld article on the teaser trailer released 7-7-09.)
2.) The Destiny stargate fully spins even though it is partially buried in the floor. (For reference, see teaser trailer at above link to gateworld or my previous post on the stargates and DHDs)
3.) The symbols on the gate are not recognizable as constellations like the Milky Way and the Pegasus stargates.
4.) The DHD is of significantly different design than the DHDs found in the Milky Way and Pegasus. (see images below)
As I've mentioned, its speculated that the Destiny stargate is one of the first designs for the gate system. It spins fully on its own, which makes the design similar to the Milky Way gates where the internal ring can spin. With a DHD, the Milky Way gates do not spin (see "Warrior" season 5, episode 18, approximately 37 minutes in) but the ring can be spun manually (or with the help of supercomputers) to dial the gate. To dial the Milky Way gates manually, the correct symbols must be aligned the correct chevron and the gate must be spun like a lock, each rotation going the opposite way. (Canon on this seems to have changed gradually from Season 1 through Season 10; each individual chevron locks with the appropriate symbol in Season 1, ep. 1" Children of the Gods", but by Season 10, ep. 17 "Bad Guys" the symbols seem to go up to the top for locking, not to individual chevrons.) The gate will activate upon the home symbol reaching the top chevron. The Atlantis gate on the other hand is completely digital in its symbol alignment. The correct symbols will rotate through like a rotary phone (which simulates spinning, but no actual parts of the stargate move) and stay with the corresponding chevron, which always reveals the full address of the wormhole, unlike the Milky Way gates.
(Please note that the SG-U Destiny stargate graphics come from the MGM Stargate Website)
If you take a careful look at the hi-res image of the Destiny Stargate, you'll notice a few differences from the Pegasus and Milky Way gates as well. The symbols, outlined in slim arches, do not seem to resemble constellations. All the symbols seem to be made up of vertical lines, shorter vertical dashes, circles, rings, and S like designs, ranging from three to five or six symbols in the combination.
Of interesting note also is that while the gate (from what we can see in the picture) has at least seven chevrons, there is another chevron glowing from the floor below and the very likelyhood that the remaining two (of the original nine that have always been on gates) chevrons are beneath the floor like they are in the Atlantis gate room. Also of curiosity is how or where the symbols lock to dial. Because the chevrons on this gate cover the entire diameter of the ring the symbols cannot spin to connect with the individual chevrons, and as we've already seen, the chevrons spin as well. The chevrons could lock at one of two places: the floor chevron or the light above the gate at the very top. It lights up (apparently) when the gate is spinning and seems to be part of the gate itself, even if not attached.
We know significantly less about the Destiny DHD, simply because we haven't yet seen it in action. We do know that its interface is not the simple "press and go" design the Milky Way and Pegasus DHDs have. By the looks of the image it seems to be a computer interface. I speculated before that the DHDs we see in the Milky Way and Pegasus Galaxies have simple interfaces so that as civilizations develop on those worlds they can begin using the stargate without necessarily knowing the Ancient language or requiring high technologies. On the other hand, there was no reason to assume that this particular DHD would ever be used by anyone other than Ancients, and so, I then conclude (assume) that the DHD, while it does dial the gate, does other things as well.
Stargate Solutions Wiki: DHDs
Wikia Stargate Wiki: DHDs
MGM Stargate Site (credit for all Destiny Stargate images)