After a lot of thought, this is what I discovered.
We try to emulate our Ascendant in time, as the Ascendant is the Mask we wear to the outside world. It is also the motivation behind our actions, after all, we are so used to the masks we wear that we tend to "project" the qualities of our ascendant, in order to well... keep up appearances.
The Sun is our individuality, the core of our persona. Like in our solar system, all the planets revolve around the sun, so do a whole lot of factors revolve around our Sun Sign.. (which is why so many people tend to think all of astrology consists mainly of our sun sign, which we know isn't true).
However, if there were a contest between which plays a more important role within a chart, the Sun or the Ascendant... well, here are two sets of arguments supporting both:
The Ascendant:-
1. More dynamic, as the ascending sign changes every two hours (approximately).
2. Once you know the ascending sign, you can gain access to the rest of the chart, as you'll know which sign falls on which house cusp, thereby getting a fairly rough idea of a persons chart (example, if a person has Gemini rising, then it's obvious the descendant is Sagittarius, and if we use the equal house system, or any other house system that equally divides the chart, we would know that the house cups are as follows - 2nd Cancer, 3rd Leo, 4th Virgo, 5th Libra.. etc).
3. The Ascendant also indicates the physical appearance of a person stronger than the sun sign (however, planets near or aspecting the ascending sign can over power the traditional ascendant features, causing one to me misguided. Example, someone with Gemini rising would be generally described as tall, lean, and long-limbed.. with a heavy Saturn influence, they would be shorter, with a Jupiter influence they would be pear shaped and unable to get rid of it, etc)
4. The Ascendant, like mentioned before, also is our motivation behind our actions. Example, someone with Libra rising would discover that majority of the things they do is to please people and appear fair and just, whereas someone with a Taurus rising would discover that majority of the things they do is because they like doing it, it gives them pleasure, and makes them comfortable.
The Sun:
1. The Sun represents our core self. This is the true individual us, what makes us unique and special. True, the sun remains in it's sign for about a whole month, but nevertheless, we all can't deny that no matter how much we don't fit in with every area of our sun sign, at the end of the day, when we dig deeper, we truly do behave and act like our sun sign.
Personal Example: I am a Capricorn by Sun, with Moon, Venus, and Mars in Aquarius, and Libra Rising. My rising sign makes me do things for the sake of Harmony, Love, and to make peace and please everyone around me, while my moon makes me rebellious and a total non-conformist. Nevertheless, at the end of the day, I am a Capricorn, plodding away up my many mountains with only the goal of reaching the summit ahead of me.
2. The Sun is the root of our vitality and our being. In many spiritual and esoteric paths, the Sun is considered the source of our life, as well as, plays a determining role in measuring our health, and our life-span. In a way, our whole world depends so much on the Sun and it's energy. Without it, the world would cease to exist as we know it.
3. The Sun also represents the true essence of who we are. Our sign represents the evolutionary stage of our soul (from infancy in Aries to 'death' in Pisces), as well as, indicates our Karmic Missions for us to fulfill within this lifetime (example: Cancer - To Nurture).
At the end of the day, different astrologers take different stances on which is more powerful, and which plays a more profound effect.
I personally believe, emulate your rising as much as you try, you can never hide your Sun for too long. No matter how thick the clouds, or how long the night... the sun eventually shall come out and shine
Love and Blessings
