A lot of factors are involved in answering your question. Speaking generally though, Moons in Virgo/Libra don't inherently stir intimidation in each other. Whenever planets are in neighboring signs, there is an emphasis on how they go about their business differently. Where both may seek involvement with others, one may fulfill that need by offering others social nurturing, while the other finds comfort proactively offering others help in a practical setting.
There is a big coin flip when it comes to neighboring signs, because their differences are what they have to teach each other. With acceptance, they can learn from each other how to uncover complexity in their own personalities. With closed mindedness they tend to just sort of frustrate each other.
The closer to 30 degrees both planets are from each other, the more pronounced this kind of relationship should be.