There are many dimensions across which we can compare music. Most people categorize music "genres" (rock, pop, hip-hop, etc.). Sometimes, we might categorize music according to its mood ("happy", "sad", etc.). In different occassions we might choose different categorizations. However, there is a categorization that escapes many people, even though it affects the music they like. This categorization is based on the distinction between complex and simple music. That is, we are talking about a categorization based on the complexity of music.
I believe that once getting aware of this distinction it is easy to see how different tracks vary across this dimension. Most modern pop and electronic tracks, for example, are relatively simple in their structure and form. In fact, this might be true for most popular songs in the 20th century (since the advent of "pop"). This might also be true for traditional music as well, since it is the closest thing to "pop" music that existed before the advent of TV and recording media.
Not THAT complex…
Classical music, on the other hand, is more complex. This is true also, for genres such as IDM and progressive metal (think of Dream Theater for example) which purposefully attempt to create complex structures (Tool is another good example) and melodies and, sometimes, even sounds.
What I have noticed through the years is that, usually, more complex music is preferred by people who had musical training themselves. I’ve also noticed that people who enjoy listening to more complex music, usually will refrain from listening to simple music.
Just like music can be categorized across many dimensions, it also affects us in many dimensions as well. Music has a very strong emotional component, but it has a mental component as well. Complex music can provide mental stimulation to those who enjoy it. It is like a hidden dimensions that requires patience and training in order to appreciate it. Most people, when listening to music, they are mostly "hearing", that is, they are not observing the subtleties in structure, form, harmony and melody. Instead, their mind simply absorbs it as a "whole".
It is just like looking at a painting. If you take a look at a painting for a minute, most likely, you won’t be able to remember every detail. You will only have a vague impression on the painting. However, this is not the way a painter would see a painting.
It is this chacteristic of music that makes it so interesting. However, while mental stimulation is can be a very enjoyable effect, listening only to complex music, has some downsides, too. Many times, people will think that listening to more complex types of music elevates them socially, or makes them seem smarter than they are. In addition, the mental stimulation could come at the expense of emotional stimulation. In that case, we are trading a dimension of understanding and listening music, for another, thus, not making ourselves richer in any sense.
I believe that both complex and simple pieces of music can be enjoyable, and there are many masterpieces in both categories. There are also many pieces of music that can be simple and complex at the same time. I believe Beethoven’s 9th symphony to be such an example. And I believe that this is an evidence of true musical genius. A genius in any field, can make the absurdly complex seem simple. A scientific discovery is nothing more than observing a pattern that seemed complex or non-existent before, but now seems evident.
In the same sense, Beethoven could create the most complex melodies and harmonies, without sounding pompous, or even difficult to understand. It is in the work of such people that the mental and emotional aspect of music are combined in a coherent whole, and I believe that any lover of music should really strive to combine these two aspects as best as he can.