Two-sided knock-out against two one-sided barriers

Compare a double-barrier knock-out option (extinguished if the price touches either an upper or a lower barrier) with a portfolio of an up-and-out and a down-and-out option on the same underlying, strike, expiry and barriers. Do they cost the same?

No, the pair of single barriers is worth more. Using $\mathbf 1_A + \mathbf 1_B = \mathbf 1_{A\cap B} + \mathbf 1_{A\cup B}$, the portfolio equals the double knock-out plus an option that dies only once both barriers have been touched. On paths that touch neither barrier the portfolio pays twice, and on paths touching just one it still pays once, so it is strictly more valuable.