What's the sonic advantage of bi-wiring

It's not always better. I don't know if it is my speakers, my amps, or the speaker/amp interface, but, my system sounds better not bi wired. It is better though using a double run of the same cables.

The cables may not make all that much difference - the speaker crossovers are probably the bigger determining factor for what if any benefit you might find with bi-wiring. There's some fairly good and accessible info at sites like Elliott Sound Products: http://lmgtfy.com/?q=elliott+sound+products+bi-wiring

I agree with the other comment above that this will depend on how the speaker was designed. Was the designer crafting the crossover with bi-wiring or bi-amping in mind? Or are those dual binding posts an afterthought, aimed at not losing potential sales t folks who may want to bi-wire or bi-amp.

Definitely biwire, no questions about it. The King will sound much better when biwired, as will the VAC amps.

I reviewed the King as well as the VAC Phi 200 amps for Dagogo.com. I bought the King following the review, as it is such a fantastic ESL, and without exception ran it biwired. You would be losing a lot of the speaker's potential if you did not do so.

The other option is to secure a very good quality jumper cable as opposed to the supplied jumpers. This will likely improve the sound nicely but I cannot say whether it will be as good as biwiring.

Now, the speaker cabling itself used for biwiring is critical; if a poor caliber of wire is used the system sound will suffer, but if you use a fine quality sounding wire your system will shine.

Theoretically, if you use the highest grade cable between your terminals as jumpers or if the crossover uses the best cable, Bi Wiring should not sound better. I've never seen 8 or 10 foot of cable sound better than a few inches of cable if equivelant cable is used throughout.
Tim