I don't really understand what Balanced means other than it's something to do with better grounding or something like that?
Balanced has a "+" and a "-" for each channel (four wires). Single end has three wires (shared ground). So the adaptor coverts the multi-pin (four-wire) plug to standard stereo phone plug (three wires).
IF your headphones have four wires (many do). The better bet is to change the termination on your headphones to the plug that matches the balanced Isabella (easily done for many headphone models).
How does balanced sound compared to single end? For a given component (like Isabella), the balanced version should have more control over the drivers in the ear phones. Typically shows up as improved bass, larger soundstage and improved imaging and detail.
I owned several balanced rigs prior to going to all RWA. So just because a product is balanced does NOT mean it sounds better than ALL single end products. But typically when a vendor offers the same product in both single end and balanced versions, the balanced comes out on top.
There's more technical stuff behind this, but the basics come down to:
Balanced amp + headphones wired with balanced plug = best sound for a given amp
Hope this helps, Kent