This is a complex issue. I think that both metrics are needed in any organization being able to define itself as "successful." Organizations that are not efficient simply are not built to last and those who are not effective are also paving their way for their own destruction.
Independently, both can be seen as important standing alone. There is something to be said for organizations that are efficient. Efficiency is usually a metric that is associated with input and output. It has a mathematical edge to it. An organization cannot be considered efficient if it is not getting more than it puts in. This is a simple metric that cuts through much in way of discussion. At the same time, effectiveness is something that organizations recognize as vitally important. One cannot be effective if the cost of efficiency is ineffectiveness in a given setting. In the end, this can doom an organization because a competing entity will be effective and thus attract more people because of it.
I would say that both are needed in today's environment. In a condition where economic progress and comfort are challenging elements, both efficiency and effectiveness are needed. Perhaps, this is a step in achieving an effectively efficient solution or an efficiently effective one. Organizations have to find a language and environment in which both are equally tempered. Efficiency and effectiveness are two ingredients that can spell long term success to any organization simply because a choice is not made. I cannot see success in today's complex and demanding environment for any organization that makes a choice between both. Seeing that today's environment is a globalized one with more consumers and competitors than ever before, an organization that makes a synthetic reality in which both effectiveness and efficiency are embraced is geared towards greater choice than those who force a choice to be made between them.