As opposed to 'rugged', I'd use the term 'rigid'.
The most obvious difference to me, when comparing brass-lined knives to steel-lined knives, is how much less bend/flex/compression there is in the handles of the steel-lined knives. The less the handle flexes/compresses/bends, the less likely there'll be issues with blade centering or rub, at a minimum (off-center blades may not be bent, but the handle might be). It'll also minimize issues like that developing over time, as knives get sat on (in back pockets) and bent or compressed. Steel liners should also strengthen pivots substantially, especially in bolsterless shadow patterns. Pivot pins are less likely to deform steel liners by bending/twisting the blade laterally as well, so that should translate into less issues with blade play, assuming the build quality is otherwise good.
David