Either - A game of preference

be able to kill anyone by writing their name in a notebook

Eliminating the world's most dangerous people—dictators, mass murderers, terrorists—directly protects countless innocent lives that healing alone never could.
There are always two paths to doing good: saving the innocent directly, or permanently neutralizing those who cause the harm.
A healer would almost certainly be captured and exploited by governments or corporations; writing a name in a notebook requires no physical exposure.

be able to heal anyone of any injury/illness, or revive the dead via a kiss

Healing saves specific individuals from illness, injury, and death—an unambiguous good that requires no judgment about who deserves to live.
Deciding who is evil enough to deserve death is an enormous moral hazard; any killing power, however justified, risks becoming indistinguishable from tyranny.
The Death Note story itself showed that absolute power to punish inevitably corrupts; the healer's power carries no equivalent risk of moral decay.
Removing one dangerous person leaves a void that another fills; healing the sick creates lasting net-positive change in the world.

Curses