Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar with the abbreviation -- indeed I have never seen a paper or a program where BIC would be used (still I admit that I'm biased to problems where such criteria simply don't work).

Edit: AIC and BIC are equivalent to cross-validation provided two important asumptions -- when they are defined, so when the model is a maximum likelihood one and when you are only interested in model performance on a training data. In case of collapsing some data into some kind of consensus they are perfectly ok.
In case of making a prediction machine for some real-world problem the first is false, since your training set represent only a scrap of information about the problem you are dealing with, so you just can't optimize your model; the second is false, because you expect that your model will handle the new data for witch you can't even expect that the training set will be representative. And to this end CV was invented; to simulate the behavior of the model when confronted with an independent data. In case of model selection, CV gives you not only the quality approximate, but also quality approximation distribution, so it has this great advantage that it can say "I don't know, whatever the new data will come, either of them can be better."

Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar with the abbreviation -- indeed I have never seen a paper or a program where BIC would be used (still I admit that I'm biased to problems where such criteria simply don't work).

Edit: AIC and BIC are equivalent to cross-validation provided two important assumptions -- when they are defined, so when the model is a maximum likelihood one and when you are only interested in model performance on a training data. In case of collapsing some data into some kind of consensus they are perfectly ok.
In case of making a prediction machine for some real-world problem the first is false, since your training set represent only a scrap of information about the problem you are dealing with, so you just can't optimize your model; the second is false, because you expect that your model will handle the new data for which you can't even expect that the training set will be representative. And to this end CV was invented; to simulate the behavior of the model when confronted with an independent data. In case of model selection, CV gives you not only the quality approximate, but also quality approximation distribution, so it has this great advantage that it can say "I don't know, whatever the new data will come, either of them can be better."

Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar with the abbreviation -- indeed I have never seen a paper or a program where BIC would be used (still I admit that I'm biased to problems where such criteria simply don't work).

Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar with the abbreviation -- indeed I have never seen a paper or a program where BIC would be used (still I admit that I'm biased to problems where such criteria simply don't work).

Edit: AIC and BIC are equivalent to cross-validation provided two important asumptions -- when they are defined, so when the model is a maximum likelihood one and when you are only interested in model performance on a training data. In case of collapsing some data into some kind of consensus they are perfectly ok.
In case of making a prediction machine for some real-world problem the first is false, since your training set represent only a scrap of information about the problem you are dealing with, so you just can't optimize your model; the second is false, because you expect that your model will handle the new data for witch you can't even expect that the training set will be representative. And to this end CV was invented; to simulate the behavior of the model when confronted with an independent data. In case of model selection, CV gives you not only the quality approximate, but also quality approximation distribution, so it has this great advantage that it can say "I don't know, whatever the new data will come, either of them can be better."