We prove that any non-Sasakian contact metric (��,��)-space admits a canonical ��-Einstein Sasakian or ��-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of ��and ��for which such metrics are Sasaki-Einstein and paraSasaki-Einstein. Conversely, we prove that, under some natural assumptions, a K-contact or K-paracontact manifold foliated by two mutually orthogonal, totally geodesic Legendre foliations admits a contact metric (��,��)-structure. Furthermore, we apply the above results to the geometry of tangent sphere bundles and we discuss some topological and geometrical properties of (��,��)-spaces related to the existence of Eistein-Weyl and Lorentzian Sasakian Einstein structures.