The two museums are not very interesting, even though one houses the Phra Kaeo Don Tao, a supposed 'copy' of the Emerald Buddha and made at the same time. But it lacks most of the subtlety of the Emerald Buddha, and the setting doesn't do it justice. For a close-up look at the Emerald Buddha, you're better advised to visit Wat Phra Kaeo in Chiang Rai, where they have a recently made copy in a beautiful setting. However, there is a beautiful 400 year old scripture library in amongst the museums that is worth a look.