A little digital compact is not able to shoot at ISO 3200 with low noise, so you'll end up using flash for indoor shooting which ruins the mood. It will not be able to shoot at 5 FPS, which is the only way (in my experience) to consistently get candid shots with magical looks on people's faces instead of closed eyes or momentary grimaces. And it won't be able to shoot with a narrow depth of field, which makes portraits way more beautiful.
If you take a nice DSLR, put it on aperture-priority with the lens all the way open at high ISO, turn the flash off, and shoot at 5 FPS while interesting things are happening to people (preferably from a bit of a distance so things are more candid), you'll get shots that people beg you for copies of. When I do this at weddings, I've have two different couples (friends/family) tell me that they liked my pictures better than the pro who they hired, and I'm not really that talented.