As John mentions, call is certainly the best way to separate these two. The buzzing call of Bright-capped is very distinctive.
Other features people haven't yet mentioned:
Habitat - Bright-capped tends to occur in drier grassland (especially hillsides).
Behaviour - Bright-capped is usually much shier, diving into the bottom of grasses, whereas Zitting will often perch near the top of the grass.
Structure - The tail of Bright-capped is slightly longer, looking a bit more prinia-like.
Head pattern - The eye of Bright-capped stands out against the plainer face (probably due to the lack of white supercilium). Most of the face is plain rufous, with the nape contrasting with the darker crown and mantle. The cheeks tend to look slightly grey, but still rather plain.
Underparts - Often a bit more contrasting on Bright-capped, which has slightly darker flanks but white centre to the belly.
