The XPS 13 features the latest processors from Intel -- the eighth-generation chips. Significantly, even the Core i5 processors in the latest generation are quad-core for boosted performance. The new XPS 13 comes with options for the eighth-gen Core i5 (up to 3.4GHz) and Core i7 (up to 4GHz).
Apple's update to the MacBook Air last June was focused on upgrading the processor. But rather than updating to the latest generation of Intel processors, Apple just included a faster processor from the same fifth-generation line of chips that the MacBook Air has used for several years. The standard MacBook Air now sports a 1.8GHz Core i5 processor from Intel's fifth generation, rather than the previous 1.6GHz Core i5 chip. Apple also lets you configure the MacBook Air with a 2.2GHz Core i7 processor from the fifth generation. But no matter what you do, the MacBook Air at this point is going to offer a lot less horsepower than the XPS 13.