What Scoob & Chuck said. In reference to what Chuck was getting at earlier, make sure right is right (sounds from the right side are favored in the right channel) and left is left by checking both the SBD recording and your microphone recording to make sure they have the the same 'sidedness'. If stuff in the SBD is too hardpanned to one side or the other you can narrow the SBD contribution by panning it's left and right channels closer to center, leaving your on-stage or AUD pair fully hard-panned to either side. You aren't likely to get phase-problems from doing that if necessary.
Lately I've been running XY because I thought there was a "phasiness" when mixing my DIN or PAS recordings with the SBD. I've been widening the AUD feed in post for a little better spread, but I wonder what opinions are here on the best configuration for cardioids when you'll be mixing with SBD.
X/Y mostly helps to counter phasiness when you need to significantly narrow the panning of the AUD pair (like for mono compatability), or are mixing that X/Y AUD pair with other AUD microphones. When mixing an AUD with a SBD there tends to be less Left-Right stereo combination phase conflicts, although there can still be phasiness between the two sources, see below* so an X/Y config is not necessarily advantageous to reduce phasiness when mixing with a SBD over a spaced config.
When mixing with a SBD, I prefer an on-stage or AUD config with some space between the microphones because that tends to provide more of a feeling of space and openess in the mix than X/Y cards usually will. The spacing helps decorellate the reverb and ambience and open things up, similar to increasing the width of the AUD like you mention you've been doing. The 24" split of the setup Ultfris describes helps provide that kind of 'good' phase decorellation.
*Take some time to play around with the micro-time alignment between the two recorded pairs, likely necessary with an AUD + SBD, maybe not be strickly so with an on-stage pair + SBD, but it still may benefit strongly from some careful tweaking. You will get significant phasisness/tone/reverb/slap-back effects when that pair-wise time-alignment is off, depending on how far off it is, regardless of what AUD config you use.