Logically, efficiency should win out over alacrity because haste makes waste. Working too quickly without planning properly will result in less accomplished overall.
However, we aren't dealing with the physical world, we're dealing with avodah. Why is it different? Because it bears with it implicit emunah that HaShem knows best and guides things to their ultimate outcome. We have to put in hishtadlut, effort, but the success of our efforts depends entirely on HaShem. We don't always know what it is we really are supposed to accomplish. If we were to wait around to try and plan with greatest efficiency, we might never leave the planning stage, whereas if we start to act with proper emunah, HaShem will ensure that we accomplish whatever we are truly meant to accomplish.
So, even though it is counter-intuitive, it pays to work first on our midah of זריזות - alacrity, and only afterwards, once we are already involved in avodah, should we turn our thoughts gradually to how to improve the efficienty (יעילות) of our avodah.