Efficiency keeps you fit; and Effectiveness keeps you at the right direction.
Enterprise Architecture is an approach to ensure enterprise as a whole is better than the sum of pieces. However, what do we mean the “BETTERNESS”? Should EA be more about efficiency or effectiveness?
Approach the question from the perspective of Theory of Constraints, ToC takes seriously of the notion that a system is more than the sum of its parts, etc. that all elements of a system constrain one another. Having a quantitative way to look at efficiency and effectiveness through some kind of framework like ToC really makes sense. Now in business you have the paradox of Synergy versus Responsiveness, and speed vs. stabilizability. That implies that EA will follow the decision of the enterprise strategy more leaning to one or the other.
Efficiency is typically achieved through standardization. The bad side of standardization is that, by definition, it eliminates potential for mutation and innovation. Consequently, standardization can foster brittle systems! When applying ToC theory to the management practices, the practical result of TOC approach is that either you are optimizing for the whole or for the parts. Local efficiencies may not add up to the efficiency of the whole and, in most cases, undermine the efficiency of the whole. The efficiency of the whole is governed by the capacity of the constraint or constraints. In effective organizations, there will be very few governing constraints.
Effectiveness, then, is a measure of how the system serves the constraints so as to maximize throughput and minimize expense. Very serious challenges to effectiveness emerge when having local measures of performance competing with global measures of performance. In short, the question is much more problematic than it appears. Specifically, regarding IT systems, the capability of measuring everything often undermines the effectiveness of the whole organization because of the many competing performance measures
At some point in the enterprise evolution, business effectiveness and efficiency are also correlated specifically when the organization reaches its capacity. At this point trying to improve effectiveness brings down efficiency and vice versa. The corollary is true as well. Obviously when they are not correlated, the organization has slack.
Generally speaking, you have to have effect first, and then make the effect more efficient. Accordingly, the next level should be on effectiveness of improving effectiveness, which could implicitly involve efficiency of improving effectiveness, and ultimately reach the enterprise agility.