Baroque a.k.a. Ultima is a chess variant in which all the pieces except the kings have quite different powers than in regulation chess. They all make non-capturing moves like queens (except the "pawns" which move like rooks and the kings which are just normal kings), but each piece has its own weird way of "capturing". The game is played on a normal chessboard with a normal chess set except that one rook on each side is turned upside down: the queen is a withdrawer, the bishops are chameleons, etc. The object is still to checkmate the enemy king. The rules can be found at the Wikipedia page.
Back in the 60s I had a friend who was much better than me at chess. We often played chess variants, including baroque, and on occasion we even played chess vs. baroque: one player would have a set of normal chessmen, the other had a "baroque" set with king, withdrawer, coordinator, immobilizer, leapers, chameleons, and pinchers.
Given the great dissimilarity between the two armies, chess vs. baroque is hardly likely to be a balanced game. Almost certainly one side has an overwhelming advantage. Nevertheless, to my humiliation, I always lost, whichever side I took.
Question. Which side has the advantage in chess vs. baroque?
Clarification: checkmate, or capture the king?
According to the rules of Baroque Chess on the Wikipedia page,
The objective of the game is to capture the opposing king.
I'm not sure if that's how I was playing Baroque over 50 years ago. In Chess vs. Baroque, it seems only reasonable that either both sides should be playing to capture the king, or else both should be playing with regular check, checkmate, and stalemate rules. As a chessplayer I guess I'd slightly prefer both sides playing to checkmate, but if you find it more convenient to have both sides play to capture the king, that's fine, and I can't imagine it will make much difference to the answer. I guess capture-the-king is easier to program, if you're going to try analyzing with a machine.