As EmRR mentions, sometimes the best alignment is a slight misalignment. I like to start by getting it as close as possible, then shift it around by ~millisecond increments while listening, going with whatever sounds best.
The when and why? There is a number of things going on-
It will depend somewhat on the relationship of the AUD and SBD in terms of how much direct-arrival content is shared between them and how similar it is (that is, direct-arrival of band sound, not direct-arrival of audience and ambient sound present in the AUD but absent from the SBD). The SBD provides dry close-mic'd direct-arrival sound, maybe with some 'verb on it, while the AUD generally contains some combination of direct-arrival and reverberant sound. The AUD provides the reverberation and reverberant tail, while both AUD and SBD typically provide direct-arrival content, and that relationship is key. An AUD pair of omnis is less likely to require precise alignment (or rather, may allow for more misalignment, intentional or not) with the SBD than a pair of PAS hypercards from the same AUD location.
When there is a lot of clear direct-arrival band sound in the AUD, misalignment with the SBD acts somewhat like slap-back echo. When the AUD is dominated by reverberant sound, misalignment of the two acts more like the
predelay control on a reverb unit. That control over the predelay-like aspect is where EmRR's comment-
"I frequently make a large room smaller, but not all the way to 'reverb emanating directly from band'." comes into play. The closer the alignment, the less pre-delay before the reverberant tail occurs, emulating the acoustic behavior of a smaller room.
In the impulse over time graph below, this relates to changing the distance between the direct impulse and the early-reflections/late-reverberation part. Apologies for the huge image.
Slapback echo comes from misaligned direct impulses. The room size / pre-delay aspect relates to the gap between the direct impulse and the reflections and reverberation portion that follows.
More on some esoteric aspects later..