While I can't comment directly, as I've always owned the fully "Maxxed-Out" version of the K&K - I will say that every incremental upgrade I've installed over the years has reaped huge dividends on the overall sound - better from top to bottom. That said, Kevin is a fairly modest understated designer, and when he says something is better, it generally means several orders of magnitude better. The difference between the standard kit and the premium maxxed-out version would most likely be in the degree of sonic refinement, via use of higher quality transformers and parts throughout the signal chain - the Cardas caps and Audio Note tantalum resistors alone are a pricey upgrade. Couple that with the Lundahl mains transformer and choke, and you begin to creep up toward the more expensive model in a hurry. As you know, the devil is in the details.
How big is the leap between the two versions sonically? I honestly can't say. If you give Kevin a call, I'm sure he'd be pleased to answer your questions.