Can you be more specific about the type of models you're fitting? Typically (though not always) models are fit by minimizing the negative log-likelihood, and for discrete outcomes, the Pearson's chi-square statistic is calculated afterwards from the observed vs. expected values as a measure of goodness-of-fit. This is not to be confused with the *deviance*, another goodness-of-fit measure, which is -2(log-likelihood of full model - log-likelihood of saturated model).

Your statement "chi-sq (modelA) - chi-sq (modelB)" would be more accurate as "deviance (modelA) - deviance (modelB)", since the deviance of individual models is not typically chi-square distributed. However, provided the sample size is large, the *difference* in deviance between nested models will be approximately chi-square distributed under the null hypothesis that model A = model B. This resulting chi-square statistic will have df(diff) = df(model B) - df(model A), as you correctly specified above.

If you compute the p-value for your chi-square statistic, and conclude that it is sufficiently small to reject the null hypothesis, then that would be an argument for preferring model B, which describes the data better.