The two indices, while similar some ways (there are overlapping data sets for instance), are fundamentally different in that EPI applies a proximity to target approach, which tells you if a country is getting closer to some absolute bench mark of sustainability (for the measures we have data for), and the ESI only tells you how a country performs relative to other countries. It cannot tell you whether the country is getting closer to some defined level of sustainability.

Section 5.2 of the 2010 EPI report compares results with the 2005 ESI, see http://www.ciesin.columbia.edu/repository/epi/data/EPI_2010_report.pdf