best similarity measure for images with different angles
A brute-force method is simply to try all rotation angles and decide if 2 images are a rotation of one another.
However, there are features (eg fourier coefficients) which are rotation-invariant. So comparing these rotation-invariant features is a similarity metric for determining if 2 images are a rotation of one another.
References:

Rotation Invariance in Images
Rotation invariant indexing of shapes and line drawings
Which Transformation, Or Similarity Metric, Is Rotation, Shift and Scale Invariant?