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The way I determine piece values it to have the computer play itself from a start position with material imbalance. E.g. to determine the value of the Archbishop (BN), I replace the Queen of one player by an Archbishop, and have the engine play a couple of hundred games agaist itself (where in half the games white has the Queen, and in the other half black. Say the side with the Queen scores 63% in that match, I then know that A < Q. To make it more even, I then delete the f-Pawn of the side with the Queen, so that I play with an imbalance of Q vs A+P (plus all other pieces present), again a coupleof hundred games. Then the A+P scores 55%. I then know that the Pawn mattered 18%, and having Q instead of A matters 13%, so about 0.75 times as much as a Pawn. Apparently the Queen is wourdth 0.75 Pawn more than the Archbishop, say 9.50 vs 8.75.

If 8.75 that is not the value I had given the computer before playing these matches, the result is unreliable, because the side with the Archbishop could have traded it unfavorably, thinking it had a good deal. (E.g. if I had told it that A was worth 6, it would be happy to trade it for B + N, while in real life it should avoid that.) I then have to redo everything with a better instructed computer. Fortunately the result that you get out isn't very much dependent on what value you originally put in, because even if the computer is misinformed to think it should try to trade A for B+N, the opponent with the Queen will share that misconception, and try to avoid these trades. So as long as both sides attach the same value to the piece, the outcome of the match will not be very sensitive to the value. Even if your initial guess was completely wrong, using the value derived from the result of that match as programmed value for a second match usually confirms that value. And once you get a consistent result, you can trust the value.

To make the measurement more reliable, you should not just compare the value against one material combination, but against several ones, e.g. not just A vs Q, but also A vs R+R, A vs B+B+N, A vs N+N+B, etc.

If the rules are different, you can still use this method, provided you have a computer program that plays by these rules, and is sufficiently strong. I am not sure which type of rule differences you have in mind. Variants with drops are problematic, because there the pieces tend to change owner so fast that an initial material imbalance very quickly changes. But in, say, 3check material is just as well conserved as in normal chess games, and you ca use the same method, and even attach a value to the number of checks by, say, giving a side that only needs to deliver 2 checks one less Bishop, to see whether the first check is wrth more or less than a Bishop.