need to know type of disc, type of pads, type of inner cable, type/amount of lube on inner cable, state of wear of disc, caliper type, brake lever type, whether the whole outer was changed (or just the visible bit), amongst other things. Also if the caliper is old, new, and/or has been overhauled recently and/or the caliper alignment checked/reset.
FWIW degreasing used discs is not always sufficient; if they have been contaminated with (say) chain lube, even in small quantities, it can bake on to the discs to make a kind of varnish, which degreaser won't necessarily remove, but that will degrade brake performance. In at least one LBS near me, if the discs are suspected of being contaminated that way, they are usually replaced if the brake shows the slightest signs of weakness and this kind of contamination is suspected.
The small rear disc will be (assuming the brake track is 15mm wide) about 125/145ths as powerful as a 160mm disc, i.e. about 15% less.. Likewise if there is a mismatch between the brake lever and the caliper then the brake power might be less than normal. These things are liable to be overlooked in a front brake, but once the added cable losses in rear brake are factored in, the rear brake can be pretty rubbish when compared with the front.
cheers