Using HHI or concentration ratio has the advantage that we have a huge comparative material. Many institutions calculate these indicators and thus you can compare the results.
In contrast, the usefulness of a number of indicators of concentration is questionable. In practice (central banks, banking supervision) are used the simplest indicators, which the interpretation is intuitive.
I do not know whether there is a better measure, but there are many.
I counted 14 indicators of concentration in banking industry (eg. HHI, CR5 (10, 15), entropy, Rosenbluth index (or Hannah and Kay), the Gini index even) and I came to the conclusion that: indicators of lower information requirements (eg. CR5) provide estimates of the degree of concentration as accurately as indicators requiring collect more data (eg. HHI). Compare the graphs in attachment.
You can then venture to say that better indicators are simpler ?!
Using HHI or concentration ratio has the advantage that we have a huge comparative material. Many institutions calculate these indicators and thus you can compare the results.
In contrast, the usefulness of a number of indicators of concentration is questionable. In practice (central banks, banking supervision) are used the simplest indicators, which the interpretation is intuitive.
A concentration measure is a tool; and the tool is appropriate for some jobs, not others. As a predictor of merger effects, it doesn't work very well, and the market structure analysis (delineate a market, then computing concentration) has largely been replaced by modeling: fit a model to what you can observe (the pre merger world), and then use the model to predict that which you cannot observe (the post merger world). Depending on how firms compete (bargaining, bidding, prices, quantities, advertising, promotion, capacity), you get different analyses. Models tell you what matters, why it matters, and how much it matters.
Werden, Gregory J. and Froeb, Luke M. Choosing Among Tools for Assessing Unilateral Merger Effects. European Competition Journal 155 (2011). SSRN