[im3w1l]

If you sort primitives then three-way maybe just two two-way comparisons. But when you use lexicographic ordering of strings or of multiple fields, then two-way will need to use three-way comparisons internally to know whether it is done or needs to move on to the next field/character. In this case three-way and two-way comparisons have almost the same cost.

Edit: For primitives we can also consider what happens in the processor. A comparison consists of two parts. First loading the operands and comparing them (loading is the expensive part here), and then a conditional branch instruction. A three-way comparison only loads the operands once and so has the same memory pressure but it does put more stress on the branch predictor. Not quite twice though, because the second branch instruction will only be encountered about half the time, and it will usually take the same path as elements are usually not equal.