Two reasons this is different:
One, Cunanan wasn’t military. A mil or ex-mil guy is going to have *way* more training in dealing with mental stress.
Two, Dorner specifically and exclusively went after law enforcement, and is former LEO himself. He knew going into this that the FBI was going to be after him the minute he enacted his plan. He therefore was already prepared to deal with the potential pressure. Knowing their methods ahead of time no doubt makes it easier for him to not worry, since he can more or less anticipate what they are going to do in any situation.
I’m ex military and ex law enforcement and I can assure you a full on hunt by the FBI will turn your life into misery. Staying in a condition Red mode 100% of the time will drain you down fast and eventually you’ll drop your guard or make a mistake and thats just what they’ll be waiting for. They eat good and sleep well at night you won’t have that luxury.