The Desire HD is much much better than the Desire.
The interface is better; HTC Sense on the Desire HD is a generation ahead of that of the Desire. And no, HTC doesn't update HTC Sense on their older phones even if they update the base Android OS diligently. That's their catch to you upgrade or pick the latest models.
The Desire HD is faster. Partly because there is better optimization on the HTC Sense; still the original Desire itself is not a slouch. Partly because it has more RAM, starting wtih 768mb. And partly because it has a better GPU, which draws graphics faster.
I don't have one, but the reports I get is that the Desire HD sips less battery than the Desire. Even though the Desire has a smaller screen, OLED actually consumes more power if apps, wallpapers and widgets have bright colors, themes and backgrounds. OLED can save battery, if you use dark themed apps. For example, Twitter for Android and Facebook both use blue on white backgrounds. That eats more screen power. Its one of the reasons I use Twicca, which is a black themed app,
The Desire HD uses an SLCD screen. The colors and contrast are not as bright, but the pixels seem sharper without the pentile formation the OLED uses. Like conventional LCDs, SLCD has a constant power draw regardless of how bright or dark a screen is. In OLED, each pixel has its own separate lighting diode.
The other factor is that the Desire HD has a CPU made of the 45 nanometer process while the Desire CPU uses 65. That means considerably smaller transistors on the Desire HD, which in turn consumes less power and a lower voltage to run them.
A killer reason for picking the Desire HD over the Desire is that the Desire HD has at least 1GB of internal phone memory to install apps on, while the Desire only has 131mb of spare internal phone memory. Froyo lets you install apps on the SD card, but the apps has to have that permission. Many apps still don't let you install on the SD card, so you will quickly run out of phone memory on the Desire and you have to constantly manage apps and memory, like deleting apps you don't need, or clearing out app caches to make more room.
While the larger screen of the Desire HD is more of an inconvenience on the pocket, it is also much easier to read and type on.
Yet another reason is that the Desire HD has an 8mp camera that is multicoated and better than the 5mp on the Desire. It also has a much better camera app to match.