Question: I have two models, one restricted, the other full. Is there a test-statistic decision criteria I could use to make a decision as to which model might be better?

Answer: 
The easiest way is likelihood ratio test if the models are nested, i.e. if 6 variables contain 4 variables. You get likelihood ratio for the 6-variable model as unrestricted. Then get likelihood ratio for the 4-variable model as restricted. Then plug into the test and get the statistic.
To expand a little on Aksakal's answer, you could use AIC (Akaike information criterion) or BIC (Bayesian Information Criterion) to make this distinction. 

$$
AIC = 2k - 2ln(L)
$$

Given $k$ parameters and $L$ maximum likelihood. Though depending on the sample size you are looking at, you may have to penalize more strongly for additional parameters such that

$$
AICc = AIC + \frac{2k(k+1)}{n-k-1} 
$$

These formulas directly from [wikipedia](http://en.wikipedia.org/wiki/Akaike_information_criterion). You will be looking to minimize the AIC. 

This is how I would approach model selection, though it does not give a test statistic and a P value such that you have asked for. The methods for model selection are many and varied, and you can read about several [here](http://en.wikipedia.org/wiki/Model_selection). To get a test statistic, you may want to look into [$\chi^2$ model selection](http://annales.ensae.fr/anciens/n30/vol30-06.pdf). Another possibility, if you have a binary response, would be to look into [ROC curves](http://en.wikipedia.org/wiki/Receiver_operating_characteristic). If you build two ROC curves for your two models and test for a difference using, perhaps, the Delong et al. approach for correlated (read: built from the same data set) detailed in R. If there is no significant difference, then the model with more parameters is not a significant improvement over the original model. 

Hope that gives you something to think about. Good luck!