Generally speaking, the two things that make magic hour lighting so special are its angle and its color. When the sun is high in the sky during midday, shadows are short and the light is neutrally "daylight." But during the magic hours the light is low in the sky, making it more directional, producing shadows that exaggerate shape and texture and generally make photos look more interesting. Since the light from the sun travels through more atmosphere at this low angle, it also changes color and becomes warmer. This is the same function that creates beautiful sunsets: light bounces off of particles in the air that change its color—sometimes dramatically.
But not all sunrise and sunset light is especially directional. In fact, this speaks to one of the subtle differences found in sunrises and sunsets: the fact that there's a difference between dawn and sunrise, as well as the difference between sunset and dusk. Generally speaking, dawn refers to the time when the sky in the east begins to lighten prior to the moment the sun peeks over the horizon. That moment is sunrise, and the light from this point on becomes strong and directional. It's the same as the difference between sunset and dusk, dusk being the time after the sun has dropped below the horizon. The crux of the issue is simple: with the sun visible above the horizon, the light will be strong and directional, producing more distinct shadows. But with the sun hiding below the horizon, the entire sky glows softly with directionless light. Whether it's pre-sunrise or post-sunset, this is referred to as twilight. And this type of light, obviously, produces a considerably different picture quality than directional golden sun rays.
Different quality of light, different type of picture, same basic time of day. This is something important to think about as you prepare for sunrise or sunset sessions. If you're visualizing directionless light, you need to work prior to sunup or after sundown. If you want strong warm rays, however, you need to be sure to shoot before the sun dips below the horizon.
Generally speaking, sunrise light also tends to be a bit cooler in color than sunset light. This is because the literally cooler air has not yet been heated by the sun, and so there are fewer particles floating around and changing the color to the golden sunset glow. That's not to say sunrise light is bad; it's obviously often quite stunning. It's just that if you want the maximum warmth, go for sunset.
Sunset also makes it easier to set up for a shot. Think about it; if sunset's at 6:15pm, you can start preparing at 5:30 under a perfectly illuminated sky. But if sunrise is at 6:15am and you want to set up at 5:30am you're going to be finding your location and setting up your gear—not to mention composing what you think may be the perfect composition—in the difficult dark of night. That makes sunset an obviously easier choice, but in most cases it isn't the ease of a photograph that people remember. So if the shot requires sunrise, you'd best suck it up, set the alarm and bring along a flashlight.
Sunrise and sunset differences also affect the direction in which you may want to set up for a shot. An east facing architectural façade, for instance, may not be illuminated by warm direct sunset rays prior to sundown, but it will be after sunup. And if you have to work at the end of the day, simply wait for the sun to set behind the structure and allow the directionless glow in the twilight sky to work in your favor—essentially, understanding that while sunset light may be too directional for your purposes, twilight might just be perfect. As long as you understand what the light is doing during the different times of the magic hours, you can craft specific pictures that perfectly meet your needs. And since it's as reliable as the sun, you can do it every day—as long as the weather cooperates.