It's not better at all. Flames of emotion make Natsu stronger the more emotional he gets. Since Natsu was obviously stronger when he fought Zeref, that's proof that he was more emotional too. Zeref tapped into all his rage, sorrow, and darkness he's accumulated over his lifetime. Not just for that particular day.
Yes, we do know that Natsu gets stronger the more emotional he becomes. Erigor noticed that Natsu can turn his emotions into MP when they fought. Ignia immediately noticed Natsu got stronger with his emotions when he went to punch him. Witnessing the attack Natsu used with Flames of Emotion was how Erigor came to the realization that Natsu is a dragon slayer. It may not be part of Atlas Flame's or Ignia's dragon slaying magic. But it is part of Natsu's.
Savage flames is literally flames of emotion. I do mean this
literally.
荒ぶる感情の炎 (araburu kanjo no hono) is the kanji that Zeref said.
荒ぶる (araburu) means raging/rampaging/fierce/savage.
感情の炎 (kanjo no hono) is "flames of emotion".
"Savage flames" is just flames of emotion that is....well, described as being savage.