Safer for the good guys, in general
If the police are on their way, and especially if SWAT is on the way, it's safer for everybody if the citizenry stay indoors and behind cover.
It's safer for the citizenry, in case there is a crossfire. Bullets may miss targets or go through light masonry and hit anybody nearby.
It's safer for the police, because they will have less of their attention distracted by trying to figure out if the onlookers or neighbors are BG's, and will be able to focus on the house in question. Then again, it's safer for the neighbors to not run the risk of being mistaken for BG's.
There are some places where police response is likely to take a long time, maybe too long a time. For instance, one of my cousins used to live in an area where anticipated police response was something like 20 minutes (semi-rural, and a small PD). This estimate was provided by one of her local police officers, who advised her to keep a gun at hand (since her then-teenage son was being threatened by local thugs). In such a case, assuming I knew the neighbors (so I know they aren't running a meth lab, or so I can tell resident from home invader, etc), then I might have to consider providing direct assistance. However, I am not trained for house clearing, and have to accept that I could make matters worse, by adding an armed variable to the mix.
If I did feel like something had to be done by me, and now, now, now, I'd make sure to let the 911 dispatcher know that I was going over there, and give them a good description of myself.
In any case, if I had loved ones in my own home, I'd want them in the safest room possible (IE furthest from the action), and probably have them armed with my 12ga and a handgun or two, plus a cell phone.