Why does the healing ability not help Subah Nur?

The two uses of powers were not similar.

In X3, Jean is reluctant to use her Phoenix powers against Logan. She holds back, out of moral and emotion conflicts. She's spent her entire life trying to snuff out the Phoenix side of her, and in that timeline, Xavier has put mental blocks on her to protect everyone and herself from that power. And all the instability from this lead her to want to die. She let Wolverine live so he could kill her, rather than let the Phoenix power take over.

In Apocalypse, Xavier has not placed any blocks on her in this timeline. She's mentally better than in the original timeline, having grown up in a more forgiving time without widespread and open mutant hate. She's younger, and under attack by someone who just wants her dead. She's being encouraged by Xavier and the life or death situations they are all in. She wants to live, and as the Phoenix hasn't been locked away, she's able to access all of its powers against someone she knows is a threat to everyone. She is not conflicted.

The two situations are a mentally stable person under attack, fight (Apocalypse) vs an unstable person that doesn't want to kill or hurt people she loves, flight (X3).

Also, Apocalypse was under the attack of multiple of the strongest mutants on the planet. He was completely overwhelmed. As far as we know, the Phoenix attacked him on both the Astral plane and the physical one at the same time as well, breaking his concentration.

Also, also, Apocalypse was weakened from being in the same body for a few hundred years. This is related to his comic back story, which is hinted at but never fully disclosed in the movie. Xavier tells Jean this right before she brings out the Phoenix force. The reason he's weakened is that his powers provided and enhanced by the Celestial technology he uses, burns the body out. While he also changes bodies to gain new powers, the main reason is that he needs to in order to live. Like burning a candle on both ends for a brighter light. In the comics, he changes bodies and has to regenerate/hibernate for decades at a time.

So to summarize, a stronger Jean/Phoenix aiming to kill and a highly weakened Opponent, under multiple powerful attacks.