What is important, an effective employee or an efficient employee?

Let us define "Efficient" and "Effectiveness" Efficient "the extent to which time, effort or cost is well used for the intended task or purpose.
It is often used with the specific purpose of relaying the capability of a specific application of effort to produce a specific outcome effectively with a minimum amount or quantity of waste, expense, or unnecessary effort.
Effectiveness "is the capability of producing a desired result.
When something is deemed effective, it means it has an intended or expected outcome, or produces a deep, vivid impression" According to that If your employee is Efficient so perhaps he may be also Effectiveness even after training.

First let's expand both terms: Effectiveness of an Employee: He is goal oriented but the other entity such as time and process may do not lie in such employee.
Also effective employee qualities are similar to completing activities and meeting goal requirements.
Efficiency of Employee: Efficient employee tends to be doing things in an optimal way, for example doing it the fastest or in the least expensive way.
It could be the wrong, but it was done optimally.
But the entities such as goal, time, process orientation do lie in such employee.
Conclusion: One can easily see that both employee can be important and helpful depends on the work flow of a particular organization.

BOTH

I would say effective.
An effective employee is efficient, as " Effective (adj.): Adequate to accomplish a purpose; producing the intended or expected result." If an employee is effective and I need him or her to be efficient he or she can fulfill my expectations.
However an efficient employee is not always effective.
An efficient employee can get things done in a timely and cost efficient manner but it does mean that he or she has effectively executed what you were looking for.
It just means that he or she was able to save you time or money.
"Efficient (adj.) Performing or functioning in the best possible manner with the least waste of time and effort."

Both

In My Opinion Both these statements have equal importance in ones life:-1.
Effective employee stands for those who shows some intellectual work and produces good results.2.
Efficient employee stands for those who have the potential and capable enough to do the work in order to fulfill their requirements according to the time and target given to them.
In other words, both these statements have equal impact in employees life........Employees can be effective when they are efficient enough to achieve the target given to them........

effective

It has to be the right mix of both or an employee who is able to precisely manage effective efficiency.
An imbalance on any part would make it not worthy.

8There are employees who are efficient but not effective and some are effective but not efficient. However, I would go for the effective employee. The employee might not be that fast and furious in his or her work, but the degree of impactof the accomplishment is high. The cost of which could be reduced through other means during implementation or proper guidance from someone else. That effective employee could be taught on how to be efficient. 

Workplaces are not perfect worlds. There will never be a perfect employee. Seldom would we be able to find that perfect employee. Just pick your choice and eliminate later as they say.

In my opinion, none of the terms are able to describe a perfect employee.
Effective must be the planning and strategy, efficient must be the working procedure! With combination of both, you get a perfect employee!!!