First of all: Likelihood-Ratio-Test can only be used for nested models. So convince yourself your models are indeed nested.

Assume likelihood1 is the likelihood of the nested model1 and likelihood0 is the likelihood of the "supermodel" model0

Your test-statistic is:

T = -2 * log ( likelihood1 / likelihood 0)

This is Chi^2 distributed with dgf (parameter model1 - parameter of model0).

To test if model1 is significant better then model0, cdf(T) should be greater then 0.95 .

EDIT: Suppose your models do not differ hugley in there number of parameters if would stick with the simpler(int you case) because the likelihoods are pretty similar.