We compare nominal efficiencies, i.e., variances in power shapes for equal running time, of different versions of the Monte Carlo (MC) eigenvalue computation. The two main methods considered here are "conventional" MC and the superhistory method. Within each of these major methods, different variants are available for the main steps of the basic MC algorithm. Thus, for example, different treatments of the fission process may vary in the extent to which they follow, in analog fashion, the details of real-world fission, or they may vary in details of the methods by which they choose next-generation source sites. In general the same options are available in both the superhistory method and conventional MC, but there seems not to have been much examination of the special properties of the two major methods and their minor variants. We find, first, that the superhistory method is just as efficient as conventional MC and, second, that use of different variants of the basic algorithms may, in special cases, have a surprisingly large effect on MC computational efficiency.