No, they aren’t. Meridians and Chakras are based on two different world views. 5 Element Theory, of which Meridians form a part, arose in the Far Eastern areas around the Pacific – China and Japan have codified versions, although Korea and the other Pacific Rim countries also share similar world views – whereas the Chakra model comes from the Indian subcontinent. The two world views are very different.
What they have in common is that they are both interpretations of the way that energy travels around the body/mind/spirit system and both are, among other things, models that attempt to explain the connection between lifestyle and health. This is not to say that either refer simply to physical health. They also refer to spiritual health, general wellbeing and psychological health.
Ayurvedic medicine is based on the Chakra system. This model posits that there are three major "Doshas" - Vata, Pitta and Kapha - and that these Doshas are indicators of particular strengths and weaknesses of the mind/body/spirit system. Like the Chinese 5 Elements, the Ayurvedic approach emphasises balance between the Doshas for good mental, physical and spiritual health. The Ayurvedic approach also encompasses the concept that our homes reflect where we are in life (Vaastu), just as Feng Shui does in the Chinese 5 Elements.
So in what ways are they different?The meridians of the Chinese 5 Elements are named for the major organs of the body, whereas the Chakras are named for major life transitions. The meridians travel around the body, flowing one into the other, reflecting the cycles of the day, month, seasons and the great cycles of Chinese eras. The Chakras, on the other hand, are more like spinning vortices, like the pictures you see of galaxies or magnetic fields. As we move through life from childhood to old age, we learn the lessons of each Chakra in turn - you can find out more about this by doing a google search or you might find "Anatomy of the Spirit" by Caroline Myss useful for a more in depth examination.
Which approach is the best?They both are, depending on your knowledge, skill and understanding. Donna Eden suggests they are two different levels among many of the human energy system. They are certainly two different understandings of the way the human system works, both equally valid. The choice really boils down to what you want to do. From my point of view, the meridians of the Chinese 5 Elements is more accessible - but I have been studying this for over 20 years!