Why does Anakin/Luke's Lightsaber change colour?

As @Jared points out in the comments, differences in the color of lightsabers between the Star Wars episodes, can be attributed to post-production. There is no canonical (in-universe) reason for these color differences.

For example, and taken directly from the question that Jared linked to... ...before the last edited release on Blu-ray in 2011, it was made green (on the 2004 DVD edition). More than likely, if you are watching a copy of Star Wars that was released before 2004, you will find color differences from scene to scene. The 1997 Special Edition and original version, the same lightsaber in this scene is white.

Whenever the filmmakers have a "better technology" to make a "better" more intense blue, then that is exactly when the saber changes color.

Yes, I've noticed this and yes it has bothered me as well. Just makes for more inconsistencies within StarWars.

It isn't the only change made to lightsabers. Initially George Lucas wanted them to appear heavy, hence a wielder needing both hands to control it. Unfortunately though, for this effect, the lightsaber props must not have actually been heavy since the direction to actors was that they should "Act As If" they're heavy. Well, only a mime could pull off that kind of acting.

After a while, this also changed to become acrobatic gnomes twirling lazersticks. But I wish it hadn't, I rather like the idea that in its OFF position (the configuration resembling a flashlight without batteries) a lightsaber hilt is lightweight and can freely dangle from your belt without depantsing your desert-khakis. However if it were to POWER ON then it becomes heavy, so if you had not yet unhooked it from your carabiner clip, then let's just hope you're also wearing your Jedi robe for quick cover-up.

I wish this model was not abandoned, a heavy lightsaber implies that its plasma blade is not merely "a lightbeam" but something which can carve into a steel spaceship door. If they'd kept the heavy model, then 1977's duel between Old Ben and Master of Evil "Darth" would not have aged so terribly, becoming slow and antiquated.

Sidenote: I wonder if the filmmakers were aiming to get back to basics while making The Force Awakens, since those duels resembled those of the original trilogy.