Either birth time puts Pluto in your first house, squaring your sun and moon. This is going to give your outward personality and physical body a lot of Plutonian intensity, even if you have Libra rising.
You know what? I'd go for Libra rising, probably in a later degree than you see with the default 12:00 birth time. This will move Pluto closer to your ascendant, but keep Libra rising. Several posters have commented on your good looks. Although this might just be your genetic inheritance, Libra is ruled by Venus, the principle of attraction, and she is augmented by an exact trine to Neptune. I'll bet you can really turn on the charm-- when you want to.
If we take Scorpio rising, it would not only give a lot of intensity, but the first thing people would sense about you would be that Pluto- sun/moon square. No doubt you feel it intensely, and your social contacts find out about it soon enough, but it probably won't give you people complimenting you on your appearance.
However, the two "outside" birth times, while not changing much else in the chart, do put your sun and moon in different houses. By house, the sun is your sense of identity; where you feel most like yourself. The moon indicates your feelings, emotional nature; and in some contexts, your mother or sense of home.
The 9th house is about broading your life experience and mental horizons, whether through international travel, higher education, developing a life ph8ilosophy, or theology. The 10th house is your sense of career, or vocation in life.
Do you feel more like the true you in one house or the other? If your sun-moon sits right on your MC, you may have a strong feeling of needing to achieve greatness in your career. (Whether you do this or not is another matter!)
Your sun/moon square Pluto will give you a lot of drive and determination, either way. Unfortunately it can be an energy of "dominate or be dominated" where you construe one person's win as your loss. Ambition in the workplace is good, but co-workers may react negatively to a sense that you try to dominate them.
If we look at your Uranus-Saturn-Neptune stellium, it is in the second house of money and your possessions in the one chart; and in your third house of communications, siblings, short-distance travel, and your neighbourhood in the other chart. If you have siblings, how was your relationship with them? These planets are well-aspected, but they should give some pretty unusual relationships; maybe a lot of turmoil. What about the neighbourhood where you grew up? How would you describe your personal finances?
Then we would also see a shift with Venus, Mercury, and Mars from the 11th house of friends to the 10th house of career. So keep an eye out for such house shifts, and see which one suits you best. Of course, you can get some seeming contradictions; in losing, for example, your sun-moon from the 10th to the 9th, while gaining Venus, Mars and Mercury in the 10th. Yet each planet has a different meaning, which should help some. Venus and mars, for example, are the "sexy" planets. In the 11th, you may start up a passionate relationship with a friend. In the 10th, perhaps with a co-worker.
One other thing you might do is think about your Uranus transits into different signs and houses. Uranus rules sudden change, and the changes should happen according to the new sign and house. This wouldn't be something like graduating from high school, which affects your whole graduating class, but something more unique to you personally.
Whichever rising sign you ultimately think is the best fit, I would suggest you work with the whole-signs house system, unless or until you are able to get your chart rectified, or suddenly find an accurate birth time. [This happened to me, incidentally, after my mother died, and I went through some of her old documents and papers. Until then, I didn't have an accurate birth time, either.]