Hoysaleswara Temple at Halebidu is the essential companion to Belur. Where Chennakeshava is a living Vaishnava temple, Hoysaleswara is a grand Shaiva monument with twin sanctums, Nandi pavilions, and wall after wall of dense sculptural work.
The detail can be overwhelming, so move slowly around the platform and let the rhythm of the friezes build: elephants, lions, scrollwork, epics, gods, dancers, and battle scenes. If you can visit both Belur and Halebidu, do not choose between them. The contrast is the point.