I wouldn't describe the current KEFs particularly "bright" -- in fact, I felt that their treble (and the "presence" region) was a bit rolled-off/recessed. But, to my ears, the JM Labs were even slightly brighter and/or analytical than the Axioms. I've never listened to these brands of speakers side-by-side from each other anyway, and what I listened to were higher-end models from each brand.
At any rate, if you like clear, crisp and detailed sound with very open/airy and transparent imaging, you will be very happy with the Axioms. To beat the Axioms in these regards with other brands, you have to go for significantly more expensive models IMO.
