Others have summarized the differences very well. My impression is that lme4 is more suited for clustered data sets especially when you need to use crossed random effects. For repeated measures designs (including many longitudinal designs) however, nlme is the tool since only nlme supports specifying a correlation structure for the residuals. You do it using the correlations or cor argument with a corStruct object. It also allows you to model heteroscedasticity using a varFunc object.

Notice: I don't have enough rep to comment on the previous answers that's why I'm writing this as an answer.

Others have summarized the differences very well. My impression is that lme4 is more suited for clustered data sets especially when you need to use crossed random effects. For repeated measures designs (including many longitudinal designs) however, nlme is the tool since only nlme supports specifying a correlation structure for the residuals. You do it using the correlations or cor argument with a corStruct object. It also allows you to model heteroscedasticity using a varFunc object.