AR(1) term in OLS vs. first lag of dependent variable

[questionsab]

Why does OLS with AR(1) term give different estimation output compared with OLS with first lag of dependent variable. Both regressions have another independent variable.

[EViews Gareth]

http://forums.eviews.com/viewtopic.php?f=7&t=465

[EViews Glenn]

To expand on Gareth's link, note that the same transformation applies when you have other regressors. The induced restricted lag on the regressors means that there is no longer an equivalence between the two models, even for the non-intercept terms.

[clavat]

Probably a silly question. But in this case when you no longer have equivalence between the two models, how do you determine whether doing AR(1) or using a first lag is appropriate?