  In this paper we consider the variational approach to cactus trees (Husimi
trees) and the more common recursive approach, that are in principle equivalent
for finite systems. We discuss in detail the conditions under which the two
methods are equivalent also in the analysis of infinite (self-similar) cactus
trees, usually investigated to the purpose of approximating ordinary lattice
systems. Such issue is hardly ever stated in the literature. We show (on
significant test models) that the thermodynamic quantities computed by the
variational method, when they deviates from the exact bulk properties of the
cactus system, generally provide a better approximation to the behavior of a
corresponding ordinary system. Generalizing a property proved by Kikuchi, we
also show that the numerical algorithm usually employed to perform the free
energy minimization in the variational approach is always convergent.
