They both cause a decrease in the material's ductility. Strain hardening through plastic deformation thus causing dislocation multiplication and ultimately increasing yield and tensile strength... precipitation hardening through the formation of second phase particles (precipitates) which establishes lattice strains at the precipitate-matrix interfaces hence impeding dislocation motions and ultimately increasing yield and tensile strength.
The common limitation that they share is a maximum service temperature. In the strain hardening method, the strengthening effect is lost when recovery occurs (relieve of stored strain energy) and at higher temperatures - recrystallization, as a result of enhanced atomic diffusion. In the precipitation hardening method, overaging occurs as a result of continued particle growth - the rate of which increases sharply with increasing temperatures.
Also, both strengthening methods induce a lost of ductility, increasing the risk of fracture at low stress levels.
That doesn't seem very complete... would someone help point out anything I missed?