I haven't tried the browns but I've read that people also think the browns are closest but doesn't the browns have a tactile bump when pressed? Isn't the Topre press pretty linear?
Browns are very similar to reds. They have a very subtle patch of resistance just before the actuation point, but apart from that they're almost the same. Compared with Topre: you know that feeling of smoothly increasing pressure, then when you press the key past a point and it collapses downwards? Yeah, well browns are not like that. They're reds with a small rough spot basically.
Browns would be more of a replacement for you red board, if you find the reds too linear. They're not similar to Topre.
If you want something comparable to Topre consider buckling spring. It's not the same -- heavier, clicky, and the drop off after actuation is sharper -- but the overall effect is similar.