Ultimately it comes down to how competitive / academic the independent school is.
I agree with Herman - if, and only if, the independent school is known to be very prestigious and highly academic, then it would be worth a mention, even though direct comparisons aren't possible.
Just assuming for the moment this were to be the case, I'm not sure I would highlight it in the written case, though. A very casual mention during the hearing would be better, if a suitable opportunity arises. For example, panels often seem to enquire about alternative schools (I wish they didn't!).