It is not, each block in Bitcoin Cash can only hold 8x more transactions.
Also, and more important: it is not necessary to for it to be 1000x more efficient, because no cryptocurrency currently has such a big amount of transactions per hour. It would be more wasteful to support 1GB blocks when they would go empty.
But, and this is actually my claim, if volume transaction increases enough to saturate a Bitcoin Cash block, then they will increase block size, as many times as it is needed, as that is the proposed Bitcoin Cash strategy. In stark contrast with the Bitcoin 1MB blocks forever strategy.
(I am assuming you don't think efficiency is measured in watts per transaction, because if you do, /facepalm)