The shunt components in a multi-order crossover (2d, 3rd, 4th order) are very important sonically, but not to the same degree as the series components. Put another way, the parallel components make a major difference, the series components make a hugely major difference!
In my 2-way speakers, I use a 2d order crossover so the high-pass has a series cap and shunt choke, and the high-pass has the reverse---series choke and shunt cap. Each one is very important but I would rank them (from most important to less) like this: 1. Tweeter cap, 2. Woofer choke, 3. Woofer cap, 4. Tweeter choke. It's possible that 3 and 4 might be reversed, hard to say for sure. I am more confident about the other rankings. Of course, the crossover frequency is also important. My speakers have a 1200Hz crossover so both drivers play vital roles.
Replacing a Solen with a CAST even in the shunt position should make a very worthwhile improvement.
In my 2-way speakers, I use a 2d order crossover so the high-pass has a series cap and shunt choke, and the high-pass has the reverse---series choke and shunt cap. Each one is very important but I would rank them (from most important to less) like this: 1. Tweeter cap, 2. Woofer choke, 3. Woofer cap, 4. Tweeter choke. It's possible that 3 and 4 might be reversed, hard to say for sure. I am more confident about the other rankings. Of course, the crossover frequency is also important. My speakers have a 1200Hz crossover so both drivers play vital roles.
Replacing a Solen with a CAST even in the shunt position should make a very worthwhile improvement.