I'm not a Vedic Astrologer (so any input from a genuine one would be most appreciated) but I do study Hellenistic Astrology, which is closely related to Vedic and from which many of the techniques and interepretations in Vedic are derived.
So the first thing to point out is that Vedic and Western Astrology are closely related, in terms of their origin. The main difference lies in the continuous tradition in India, over nearly 2,000 years, whereas Western Astrology failed to maintain it's own tradition. This means that in the West, Astrology is very much a 'stop-go' history, with traditions being lost during centuries of little vibrance.
If you look at the Western tradition (such as it is) before the twentieth century, you will find that the Ascendant is by far and away the most important point in the chart and it outweighs Moon and Sun. The Ascendant (and its ruler) is the native (person whose chart it is) and the other houses show the outside world connected, but objectively independant of the native. This is the case in Vedic.
However, don't put to much emphasis on Signs. In both traditions planets are far more important and it's impossible to draw realistic conclusions without the planets and their positions in the chart.
You asked abouta Scorpio Ascendant in Vedic. I've got a bit of information from a nearly 2,000 year old text, The Yavanajatakata of Sphujidhvaja:
If Scorpio is in the ascendant, the native is a man with a broad, tall, and fat body, deep-set, reddish, blazing eyes, massive eyebrows, a low-hanging belly, and a nose that is slender in the middle; a sharp, firm, aggressive, and fierce man who is impatient of injury and whose character is rough within; a jealous person who does what his mother wishes; a hero who kills, takes, and sets up obstacles;
one who delights in injuring his friends and elders and eats (the food) of others; a fellow who tries to seduce other men’s wives; one who possesses a family and flourishing wealth; a man whose brothers are hateful and relatives low;
a man rich in sons who destroys confidence and has a bile-disease; are strained and generous man whose face is full of holes; a man who serves the king and has various groups of enemies; a person with many wives who has attained righteousness (dharma) ;
one who is righteous (dharma) even in everlasting activities and gets wealth and honour by resorting to service; a man who dies because of such things as his enemies’ killing him, his drinking of intoxicating liquors, faults, his passion for women, or imprisonment
Now if you remember that traditionally Mars rules Scorpio, you will see these descriptors are heavily 'Mars' related and you will find similar descriptions in the Western tradition, in the sense of physical characteristics and a temperament that is martial in nature. The reason for this is that the Ascendant is taken as signifying the physical body and is the main input into character traits.
It's a totally alien approach to Modern Western but, and it's a big but, this is subject to significant, if not major change, depending on where Mars lies in the chart and where the other planets lie in the chart. Thus the 'pure' 'Scorpio' may well be largely diluted by particular planetary influences, or exaggerated by different influences. The positions of other planets may modify the physical characteristics described or the temperament traits.
If you look you will see both good and bad traits (though being Mars, the good traits are perhaps less that the bad). So other factors may increase the good and depress the bad. But as in the Western Tradition, it's not primarily a character analysis based approach. It's an event based approach.
One last point. Remember that Vedic never followed the lead of later Hellenistic and Medieval Astrology and adopted the Tropical Zodiac, so Sun in 'Scorpio' will actually occur later in the year than it does in Western Astrology. When Scorpio begins in the Western system, Vedic has the Sun around 4 or 5 degrees Libra. So if you are a Western 'Scorpio' you are most likely to be a Vedic 'Libra' unless you were born in the last five days of Scorpio
Edited to add:
I gave you a 2,000 year old version of Scorpio on the Ascendant so here is a twenty first century version from Komilla Sutton, a noted Vedic Astrologer in the UK.
People with Scorpio rising are very beautiful, with a well shaped body, which can be very sexy too. There is great emotional sensitivity but there's always a sting in the tail, so you will be capable of great vindictiveness, and nurture a tendency to be secretive too. The conflict between this base self and a strong spiritual side will dominate in life.
This is more in keeping with modern sensibilities but still starts with the body and includes the basis of character.
