Other factors that would be important are:

The area of the bruise since stress is force per unit area. One would probably rather be hit with large (blunt) object rather than a pointy or sharp one of equal weight and acceleration.

Coefficient of restitution (or "give") of the step. A steel step with no "give" will hurt a lot more than a carpeted one.

Made for great mental entertainment thinking about fall physics on the train last night. Thanks for falling Mrrzy.