The K-01 KILLS the K-03 - its not even close. Better everything, from power supplies to transport to DACs, to internal clock, etc. Some of their lower-priced transports are occasionally noisy, which usually is a stray ball bearing or mis-aligned tray. Easily silenced by their factory - customer support is very strong as well. I have a K-03 in my office and a P-02 at home and both are dead quiet. Ux-1 is sometimes a little noisy - it has been heavily modified.
Also, not sure if you realize that Esoteric transports spin at 4x the speed of CD's (and most other players) in an error-correction read-ahead buffer system. The superior build quality allows them to do that for their higher-end transports.
To me, the choice would not be Accuphase vs Esoteric, but rather which model of Esoteric to get. :-) Good Luck