What's the sonic advantage of bi-wiring

Generally speaking, you can expect a cleaner sound overall with better separation between instruments. A little better imaging also. The real issue with bi-wiring is, is it worth doing? That all depends on your equipment. Most people will tell you to get a single run of a really good cable with jumpers, instead of 2 lesser runs. I feel that is the way to go most of the time. There are some exceptions, however. In my main system, I use Vandersteen speakers. They design their speakers to be bi-wired. It makes a very big difference. In my system, 2 inexpensive runs of cable sound much better that 1 really expensive pair. In my 2nd system, I have a pair of Wilson speakers. They don't believe in bi-wiring. They only put 1 set of binding posts on the speakers and don't even allow for it.

In the end, every system is different and you just have to try it. Theres really no other way. I had a pair of Martin Logan ESL's and I preferred 1 run of cable with jumpers with those speakers.

I prefer a single wire with jumpers to biwiring. I agree it really depends on the speaker and how the crossover is designed.

I have owned many, many, many speakers and outside of the Vandys, I always preferred the method above.

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.