I, on the other hand, think Ayu trumps Hikki vocally 9 times out of 10

Yes, Hikki has better technique (especially when listened to in the context of Western standards) but I prefer Ayu's more emotive and Japanese singing. It's closer to enka and old J-pop than anything else.
Vocally, I'd say Guilty was the superior album out of the three, and the most emotionally affective.
Heart Station, on the other hand, has one masterpiece of a song in it: Beautiful World. It's the best song among all three albums.
However, I find Kingdom to be a the pinnacle in terms of Koda Kumi's career. It seems she's finally made the songs she's been trying to make: for the first time the album organically combines her dance songs, ballads, R&B and cute songs. Unfortunately, the album also contains the worst track out of all three: Freaky. I'd rather have I'll Be There in it.
Quite frankly, Ayu and Hikki seemed to have reached a stalemate in their careers. Guilty sounds like the last tired gasp following the My Story - miss(understood) - secret style arc (and what an impressive record that is with each album managing to sound different, except for Guilty which sounds too much like secret). And Hikki hasn't quite moved past her Traveling - Sakura Drops - Colors - Dareka compositional themes (again, each of those manage to sound unalike each other), wherein the instrumentation seems to go on for the entire song in a steady unbroken line containing slight vocal and emotional deviations. (Compare something like Uso Mitaina with Flavor of Life. The latter comes across as lifeless.) Each track in Heart Station moves, progresses, and ends in the same way, with Beautiful World the only one that emerges unique because it is the best-made in these terms.
I vote for Kingdom because it is, I think, Koda Kumi's First Love and My Story. It's probably the best non-compilation album she'll ever make in her career. Guilty and Heart Station are decent, but I expect much much much more from Ayu and Hikki.
See? Not everyone here hates Koda Kumi