Problem with comparing GLM models having a different link function Given the same set of covariates and distribution family, how can I compare models having  different link functions?
I think the correct answer here is "AIC/BIC", but I am not 100% sure.
Is it possible to have nested models if they have a different link?
 A: For this problem you can also use so-called "goodness of link tests", the canonical treatment of which was published by Daryl Pregibon in Applied Statistics in 1980. You might want to read the paper here. 
There has also been some more recent work on that front, noteably by Cheng and Wu in their 1994 JASA paper.
As stated by @gung using the deviance is also possible, see e.g., this paper if you don't want to take it at face value. 
A: (I'm just copying the information from the comments here so that this question doesn't show up as officially unanswered.)
You can compare the two models by comparing the deviances.  All the AIC and BIC do is adjust the deviances for the number of parameters in the model.  Since that number is the same, it won't make any difference.  In general, it will be very difficult to differentiate between different link functions unless they differ in shape; it is often better to use theoretical knowledge to determine the appropriate link function.  For example, the logit and the probit links barely differ in shape at all but do differ in how you are thinking about the data generating process (as I discuss here).  
