[smu3l]

This is not correct. Logistic regression can be used for classification, true, but it can also be viewed as a way of estimating the conditional mean of an outcome variable that has a Bernoulli, or binomial distribution, depending on the formulation.

There are many ways to evaluate all of these methods, and for classification you may favor something else, but it's completely reasonable to use the (cross validated, or not) empirical risk for both logistic and linear regression. That would be a negative log likelihood in both cases, from the Bernoulli/binomial distribution for logistic regression or the normal distribution for linear regression.