[morzh]

ESR is important and is linked to the ripple current rating, and usually high ripple current caps are also low ESR, but not necessaily otherwise.

ESR contributes to the ripple rating by dissipating heat while the current travels through the cap; this is usual heat dissipation, I-square-R, but the ripple rating takes into account overall temperature regime to which many factors contribute: size, ESR, loss tangent, mass.

What ESR itself is reponsible for is producing the ripple voltage while the ripple current travels through it. This parameter is more important when a cap is used say as the output cap in the rectifier stage of a flyback converter, or at the output of a buck converter. This is where the ripple voltage is less affected by charge-discharge or capacitance than it is by ESR.

However in the full wave rectifier working from Mains due to long discharge the ripple voltage is practically not affected by the ESR but is affected by the discharge current and the capacitance. And since the ESR only indirectly points to the Ripple current rating it is better to look at the latter directly.