IMO in general a DA revolver is better for self defense. The automatic has some inherent advantages in combat but in general these are not significant in most self defense situations and are countered by a revolver's simplicity. I would qualify that with 2 exceptions:

1. For deep concealed carry you have a better ammo selection in an automatic. While you can get a .357 in a subcompact revolver that caliber is not any more effective than a .38 special in a very short barrell, and with tremendous recoil and flash to boot. A 9mm or .40 will generally be a better self defense round out of a very short barrell and are available in sub compact autos. Now that said my prefered subcompact is a 5-shot .38 special snubbie. When you move up to a compact to large size handgun though that advantage disappears and I don't think any pistol out there has a significant advantage over .357 or .44 special in terms of stopping power out of a 4 or more inch barrell.

2. the second case where an auto would be better is if you have some reason to expect an attack in force vice being a target of opportunity. For example if you are a drug dealer, carry around wads of cash or jewels or have pissed off a gang and you think you may be specifically targeted. This is no longer the typical self defense use but is essentially a combat situation and I would want a high capacity automatic over a revolver (and a rifle or shotgun over either).