If we're talking about the empire from legends continuity, the empire would destroy the reapers. The legends continuity empire had planetary system destroying weapons and excellent military commanders/strategist like thrawn.
Also remember the reapers true power was in advancing technology as they wanted, the empire would be outside that scope. Things like hyperdrive, planetary shields, energy based weapons, thousands of planets and species to fight and the force would be things that the reapers would need to contend with.
Don't get me wrong it'll be a brutal fight for both sides but the empire has it.
Well the Reapers can't stand biotics... and the Sith... well think of them as Leviathans..... they alone would take a considerable amount of Reaper Capships out of order. And the Star Wars Tech is far more Advanced than any Reaper Tech.