The utilisation of HTS composites raises the obvious question of how the stability of these materials differs from that of classical ones. The improved stability of HTS is due to the increased specific heat and a wider temperature margin between the operating and critical temperature. The quench analysis of HTS magnet system is however quite different from their LTS counterparts because of the slanted E(J) characteristic due to the thermally activated flux creep and macroscopic material inhomogeneities. The comparison of different quench parameters of a 6 T LTS wiggler and a 5 kJ HTS SMES have been evaluated. The former system is installed in a 1.5 GeV electron storage ring in the University of Lund, Sweden, and the latter has been demonstrated to compensate a short term loss of power. The stability considerations are projected to the essential quenching factors, for example normal zone propagation (NZP), hot spot temperature, current decay and internal voltage.