Exactly what it says on the tin, as the British say:
In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?
Is the answer to the previous question affected at all by the particular relative strengths of the players (as in, is the answer for a team involving Magnus Carlsen and I (probably around 1200) substantially different than that for team involving a 1600 and an 1800)?
I can think of good reasons for both: the stronger player being the hand might be nice because they could select the best move under some constraints, and thus only very rarely make an outright blunder (generally, the only way they could play an outright blunder (assuming they're strong enough to pretty reliably avoid blunders) would be is a piece was chosen that had NO good moves, which I think is probably pretty rare). On the other hand, a stronger player being the brain might be preferred, as they could narrow down a decision tree for the lesser player in the hopes that the best move might become easier to see without such a large tree to analyze.
To be clear, Hand and Brain chess is a type of team chess in which two players play each side. One (the "Brain") is only allowed to pick a piece type to be moved, and the other (the "Hand") must move that piece type without knowledge of what the first player intended. For example, if the "Brain" says "pawn", then the "Hand" must move one of the pawns. If the "Brain" says "king", then the "Hand" must move the king (includes castling).