Basis of differentiation 

Lysosomes

Proteasomes

Definition

A lysosome is a membrane-bound organelle that contains digestive enzymes

Proteasomes are protein complexes which degrade unneeded or damaged proteins by proteolysis

Substrate degradation

Lysosomes degrade cytoplasmic components, including individual proteins, defective or surplus organelles through autophagy, or protein aggregates

Proteasomes degrade individual cellular proteins in a highly targeted manner through the ubiquitin-proteasome system

Structure

They are spherical vesicles with a single lipid bilayer membrane

They are cylindrical structures with a central core and regulatory particles at each end

Mechanism 

Lysosomes use hydrolytic enzymes to break down substrates 

Proteasomes degrade proteins by unfolding them and threading them into the central core

Regulation

Lysosome activity is regulated by the pH of their environment, and have an acidic interior (pH between 4.0-5.0) which amplifies activity of hydrolytic enzymes

Proteasome activity is dependent on ubiquitin ligases