Back to the Question - Many active DI boxes have switches that can cut a signal down. These are pads. Pads are loads created with resistors and other components to cut the signal down when the input voltage is too high. A passive DI box will loose between 3 to 6dB of signal. Also, passive DI use transformers.
All transformers have a unique sound.
If your church has an NC above 42dB, the sound of the DI will not be noticeable. If the church has an NC below 42dB, then everything counts. Active DI boxes offer 0dB signal loss and since they don't use transformers, they add far less coloration to the original sound. To the best of my knowledge, there are only a few Active DI boxes that have such abilities. Generally, they should be called Active DI with Preamps.