Q:

Effect of the Tenth Doctor’s regeneration on the TARDIS

Why was the TARDIS heavily damaged when the Tenth Doctor regenerated, but when the Ninth Doctor regenerated, there was no visible effect?
Is it a writing error, or just done for plot-based reasons?

A:

The Tenth Doctor's regeneration was an unusually violent one.
It's established that Time Lords have some control over their regenerations. For example, in the classic episode Destiny of the Daleks, Romana (a Time Lady and the Doctor’s companions) regenerated about half a dozen times until she found an appearance that she liked.
In this instance, the Tenth Doctor was reluctant to regenerate. When describing regeneration, he said:

Even if I change, it feels like dying. Everything I am dies. Some new man goes sauntering away… and I'm dead.

He spent a long time putting it off, both before and after his lethal dose of radiation. Once he gets the dose, he makes a final trip to visit many of his companions, trying to keep regeneration at bay.
All that time, regeneration energy is building up. When he finally concedes, it bursts out of him in a particularly explosive way. Normally the Doctor regenerates shortly after his “death”, so there's less of a buildup.

