A modern brig looks more like a River-class OPV

Would a modern brig resemble a Type 31 frigate or a Batch 3 River-class offshore patrol vessel?

The Batch 3 River-class OPV is the closer analogy because the historical brig's usual function was escort work rather than major fleet combat.

A Batch 3 River-class offshore patrol vessel is the preferred modern comparison. The basis is the brig's usual escort role. In that sense, it is a closer match than the Type 31 frigate proposed in the question.