Comparing nested IRT models (unidimensional vs two correlated factors) I am trying to decide whether a theoretically derived (i.e. confirmatory) IRT model fits the data better than some parsimonious (i.e. exploratory) IRT model. Specifically, I have 14 binary indicators of outgroup-stereotyping. Our theory suggests that we should have a confirmatory model in which the first seven items load onto the first factor only, and items 8-14 load onto the second factor only, while latent traits should be correlated. Can I simply compare the BIC or similar criteria of this constrained model to an overall one-dimensional exploratory model? I am skeptical because differences in the BIC are HUGE (86311.38 for the 
 A: In this type of setting I prefer to use confirmatory factor analysis (CFA), which is the same as IRT just specified differently. CFA has numerous fit indices that you can use, besides the AIC/BIC, to identify which model fits the data best. If you are a R user, for example, you can use the lavaan package, and you can specify your indicators as binary (rather than continuous). Then you can compare fit using root mean squared error of approximation (RMSEA), Comparative Fit Index (CFI), etc. You can also identify modification indices to see how the model might fit better.
I can provide detailed code for doing something like this if you want - let me know in the comments. Based solely on the BIC numbers you have there, as long as the underlying data are the same, I would say your confirmatory model fits much better. However, I find when conducting psychometrics you are better off doing a bunch of iterative testing - triangulating as many measures as you can, if there are alternative models that may fit better, seeing if there is theoretical justification, looking at other item statistics (e.g. discrimination and difficulty parameters - comparable to factor loadings and intercepts/thresholds in a CFA) and seeing if all of the items behave as expected, and also looking at reliability. In sum, I would make a final model decision on a suite of statistics and tests, not on a single one - and ensuring that the content of the items that are being suggested by the data to be aligned is in fact aligned.
A: I'm answering rather than asking for clarifications in comments because I suspect the original poster won't return. I suspect the question is not using standard terminology in some cases.

I have 14 binary indicators of outgroup-stereotyping. Our theory suggests that we should have a confirmatory model in which the first seven items load onto the first factor only, and items 8-14 load onto the second factor only, while latent traits should be correlated.

That suggests the poster fit two separate IRT models with correlated latent traits. If you thought the 14 items described a single latent construct, you would fit one IRT model to all 14 items.
You can clearly use the BIC to compare both models if they are nested. They seem to be nested to me, but I'd love it if someone could confirm.

I am trying to decide whether a theoretically derived (i.e. confirmatory) IRT model fits the data better than some parsimonious (i.e. exploratory) IRT model.

I don't think I've ever heard what I presume is a one-dimensional IRT model called an exploratory IRT model. In the R package mirt, Phil Chalmers (the author) describes exploratory IRT as: you specify the number of latent traits that you think may exist, and the program estimates the loading (i.e. discrimination) of each item/question on each factor. This is a bit like exploratory factor analysis. I'm not familiar with this technique; I bring it up only because this is the only context I've ever heard the phrase "exploratory IRT". I'll presume the OP meant that they were looking at a unidimensional model as the alternative.
I'd respectfully disagree that the use of linear SEM is required to answer the original question. If the two proposed models, i.e. a unidimensional model vs two correlated factors, are nested, then the OP could just use BIC. If they're not, then I'm not sure what to use.
Linear SEM does offer more fit indices (e.g. root mean square error of approximation, Tucker-Lewis Index) which can tell you if the unidimensional model fits well enough by commonly accepted standards. (If using linear SEM, I'd be sure to use the weighted least squares estimator, which is acceptable for ordinal data; I believe that in lavaan, you just need to declare the items as ordinal factors to enable this; in Stata or MPlus you'd need to specify the appropriate estimator in options.)
Modification indices in linear SEM suggest if error terms should be correlated to improve model fit (they're normally modeled as uncorrelated). There's no parallel to this in IRT. That's another reason I think the linear SEM recommendation isn't as helpful in this context.
