That is, piston engine vs. jets...
...Hard to say, but it's easier to fit filters to piston engine air intakes. Big snag is that the filters would clog up, unless somehow you could retrofit something like a dust cyclone to the intake.
Maybe the jets (particularly early centrifugal compressor designs) would have had greater restart capability once out of the ash cloud. What stops the jet (I've read) is the 'ash' melting on fuel injectors and clogging them.
BTW, 'volcanic ash' is inaccurate - the airborne particles are like fine sand or rock fibres, in composition identical to pumice. Inhaled, they cause lung damage, ingested into an engine - it's like tipping sand into an unprotected carburettor. Engine wear is enormously increased and you'd be liable to seize up the engine.