Software development methodologies (SDMs) have had an accepted evolution (i.e., the replacement of SDMs of one era to the next) through the pre-methodology and early-methodology eras to the methodology era. But in the last 20 years, the transition of the methodology era (rigor-oriented) to the post-methodology era (agile-oriented) has led a debate on benefits and drawbacks of rigor vs. agile orientation. Regarding the general software-engineering evolution, the service-oriented software engineering (SOSE) that studies service-oriented computing (SOC) development approaches, which are widely used to develop software-oriented computing applications (SOCA), has emerged. SOSE developers then face the problem of selecting and adapting a SOCA SDM. This chapter compares 11 SOCA SDM on agility-rigor balance by a framework of Boehm and Turner addressing the rigor-agility conflicts by defining three factors and their methodological characteristics. Each characteristic is evaluated for each SDM with a novel agility-rigor 45-point scale. Results suggest three of such SDMs are agility-rigor balanced.