^ in smaller rooms, where not everything is going through the PA due to stage volume, stage + SBD (PA mix) is often an ideal 4 track approach.
What is not sufficiently loud on stage will be emphasized in the PA mix, and the opposite will be true for the stage sound (it will lack precisely those things that the FOH engineer is adding to the PA mix). If you're worried about not getting enough crowd noise w/ stage + SBD, use omnis or wide-cardioid mics on stage.
The best mic approach to take when 4 track recording should be conditioned by the size and acoustic properties of the venue, in a similar fashion to the considerations the FOH should take in setting his reinforcement mix. (Of course, other set-up limitations may further limit your options, but those are more people/management considerations vs. audio theorizing).
I think it is generally not cool to ask a FOH engineer, who is likely being paid peanuts, to do extra work and set up a recording sub-mix for you unless you're already friends or you're tipping him/her somehow. So, a fail-safe approach is to never expect to get more than a PA mix feed from the SBD (if that), and choose which mics to use and how/where you set them up accordingly.