Which is a better method of calculating development: HDI or GDP per capita?
Whenever you have two measures of something and one is more complex, the more complex measure is likely to be the better one. I would argue that this is the case with HDI and GDP per capita.
When we talk about "development," we usually mean the overall development of a country, not just its wealth. For example, a country that had oil deposits could become very wealthy in terms of GDP. But if that country did not offer its people opportunities for education and did not provide them with good health care, we would not really think of it as a "developed" country.
GDP measures only economics. The HDI at least factors in things that pertain to the quality of lives that people lead. Therefore, the HDI is better than GDP as a measure of development even though it is in no way perfect.