Answer:
Both objects accelerate, however due to Newton's 2nd law the acceleration of the rifle is less due to it's higher mass.
Newton's second law F = ma
In your question the force (F) would be the same on both objects, but the mass (m) would be different and give a different answer for acceleration (a). This difference can be seen by looking at the effect of being on opposite sides of the rifle (ie kickback vs bullet hole)