Could you take the squared difference?

Lots to choose from:

https://docs.scipy.org/doc/scipy/reference/spatial.distance.html

How do your vectors look like? What do you intend to do with them? Will you be clustering them? Indexing them? How many are there? How did you obtain them? What do they represent? What is their type?

I have classified some data points as anomaly in timeseries data and calculated feature importance vectors for them. Now I want to calculate similarity between two anomalous data points based on their feature importance vector.

Inner product between metrics tells you the projection of one onto the other. Whatever the space you're building reperesents

Try cosine similarly?

Well it also depends on whether you have sparse vectors or not... Some metrics work best for sparse vectors and other work for dense vectors. Check out scikit learn's pairwise distances metrics to understand better

If you care as you said about both magnitude and direction, try with L2 (Euclidean distance) , not cosine similarity.

You can use Cosine similarity

If you settle on the Euclidean distance (or weighted Euclidean distance) and you need to do it FAST, can I recommend the amazing MASS algorithm https://www.cs.unm.edu/~mueen/FastestSimilaritySearch.html