I bought the Supplier for my Cute Beyond. It made, at best, a subtle difference. I think I notice a little more clarity in the bass and slightly better highs, but I sure wouldn't want to bet the farm on it in a blind test. I admit that my ears are not the best, however. Other people may notice more of a difference.
There are some reviews on here that do suggest the extra power supply does make a noticeable difference. Also, Firestone has a satisfaction guarantee, I believe.
One thing that may be a factor, though, is that I have high impedance cans, where the voltage swing, as I understand it, is more important than current supply. With lower impedance, higher current draw headphones, you may notice more of a difference. Somebody with more technical knowledge than me may be able to verify or refute that theory, though.
On the positive side, the Supplier is fairly cheap, and if there were any issues with the stock supply, or your power lines, it would take care of them, I would think. It also looks good stacked with the Cute amp, which is a superficial factor, but hey, I'm shallow. I may even get one for my Fubar II for that reason alone.
Yes, I do have more money than brains, but it's not because I'm rich.