Fisher, my experience has long since led me toward the latter advice. This time last week I was in court in Arizona to speak for an armed citizen who had to shoot and wound two of three people who attacked him. He followed the "Don't speak to the police" advice, and has been under the Sword of Damocles ever since. (The jury deadlocked.) It has been a very long nightmare for him. Many who are familiar with the case believe that if he had just said a very few things at the scene, it probably would have been ruled justifiable shortly after it took place.
I personally recommend BRIEFLY establishing four things at the scene, and then deferring detailed questioning until after you've consulted with legal counsel.
1. THIS MAN ATTACKED ME. Establish from the beginning that the other guy was the perp and you were the intended victim.
2. I WILL SIGN THE COMPLAINT. Confirmation that you are the victim/complainant, and the man who forced you to shoot him was the perpetrator.
3. POINT OUT THE EVIDENCE. Evidence is perishable, and if the investigators don't know where it is,or even that it exists, the evidence that would prove your innocence may disappear.
4. POINT OUT THE WITNESSES. People are sometimes reluctant to "get involved." Those who saw what happened and can confirm your account of a justifiable shooting may disappear if you don't get the investigators talking to them immediately.
5. YOU WILL HAVE MY FULL COOPERATION AFTER I HAVE SPOKEN WITH COUNSEL. The defender who has just gone through a near death experience will very likely have altered perceptions, and is not prepared to sort out the details. Police experts in officer-involved shootings, and psychologists alike, recommend a period of time for the shooter to settle down before there is any detailed questioning.