Air and water
Air handles a feeling by discussing it and water handles it by staying in it. Libra's instinct is to raise a difficulty in balanced terms; Scorpio's is to notice what was left out of the balanced version and go after it.
There is a real complement here. Scorpio gives Libra's even-handedness some weight, and Libra gives Scorpio a way of speaking to people that does not corner them. The failure is Libra finding the intensity intrusive and Scorpio finding the poise evasive.
Cardinal and fixed
Libra opens the subject and Scorpio does not let it close. That is the pattern in nearly every disagreement these two have, and the modalities explain it better than the elements do.
Libra's method is to reach a settlement and move on; Scorpio's is to keep a matter open until it has been resolved to satisfaction, which may take considerably longer than Libra thinks reasonable. Premature peacemaking is the specific error, and Libra makes it repeatedly. Waiting out the discomfort until Scorpio has finished with a subject is the more effective approach, and it is not a pleasant one.
Venus, Pluto and Mars
Venus rules Libra. Scorpio goes to Pluto in modern practice and to Mars in the traditional scheme, and both are worth reading. Venus seeks accord, Mars seeks a decision, Pluto seeks what is underneath.
Venus and Mars have their own long-standing association, which is part of why the pairing has the charge it does. Where those two sit in the two charts, and how they aspect each other, tells you far more than the rulership diagram alone. A Libra with Mars in a water sign meets Scorpio's intensity rather than flinching from it.
Where it grinds
Trust, and how it is established. Scorpio tests, sometimes without admitting to it, and Libra experiences a test as an insult. Libra smooths, and Scorpio experiences the smoothing as concealment. Each behaviour confirms the other's suspicion, which is why the pattern hardens rather than easing.
The second friction is Libra's sociability. Libra maintains warm relations widely and lightly, and Scorpio does not have a category for warmth that means nothing. This is the argument these two are most likely to have more than once.
What the sun signs leave undecided
Almost everything. A sun sign covers a twelfth of the population, and a comparison of two such categories can only describe a tendency across a large group of pairings, not the one you are asking about.
Moon contacts govern how safe the two feel with each other, which in this pairing is the whole question. Venus and Mars govern attraction and conflict. Those comparisons are where an actual answer would come from.
Questions people ask about this
Why is there tension between Libra and Scorpio?
Libra settles a matter to restore calm and Scorpio keeps it open until satisfied. The methods contradict each other in almost every disagreement.
Is Scorpio suspicious of Libra?
Libra's widely distributed warmth is difficult for Scorpio to interpret, since Scorpio has no category for warmth without weight behind it.
Which ruler should I use for Scorpio?
Both are informative. Mars describes how the sign acts and fights, Pluto what it is trying to get underneath.
What decides this pairing?
The Moon contacts, mainly, since trust is the live question. Venus and Mars across the two charts fill in attraction and conflict.