As others have said, the LS3/5a's was a technically elegant small monitor speaker that successfully ironed all of the music out of anything fed into it, and issued forth ruler-flat tones. A party I went to years ago was notable for the reasonable mixtapes being played from a Nak, through an A60, but totally boring-ed out by LS3/5a's. Arghh. Didn't last more than an hour, we left in search of alternate cheap thrills.
The Kan, by comparison, was similar size, not at all accurate, but if fed a very excellent signal (LP12, P9, Xerses or a good two-box Naim CDP, for example) and gripped with an excellent amplifier, was quite happy to launch more music at you than was even in the signal. Even if it was a bit of a pastiche. They're fun, bouncy, like they've had a couple in the middle of the day. Depending on the recording, it might have been two pints, two quaaludes, two tabs of ecstasy, or a couple of lines. Certainly not mandrax; the Kan is always in a hurry. I loved mine (Tony's old MK1's), and still miss them some 16 years and some change, later.
FWIW, Some of my favourite small speakers include the Royd Minstrel (again, not at all accurate but *so* *much* *fun*!), the Royd Sintra, the Kans, and the Naim IBLs. Oh, and I still have a penchant for ES11s. Any or all of the above will play music in a way that LS3/5a's cannot even imagine.
PS - I really liked Rega Kytes, too.