DF test examines whether a serie is nonstationary (the null hypothesis is non stationarity) whereas KPSS test checks whether a serie is stationary (the null hypothesis is stationarity).
DF test has low power and Eliott, Rothenberg and Stock (1996) demonstrate that DG-GLS test improves the test power compared to standard DF test.
In my opinion, a good strategy consists in comparing several tests to ascertain the stationarity issue.
What do you mean by "critical value adjustment"? I check the Eviews' user guide (Guide II, Chapter 34, p. 476) and the software uses the MacKinnon critical value calculation.