...AIC/AICc has theoretical advantages over BIC...AIC/AICc is derived from principles of information; BIC is not...BIC has a prior of 1/R (where R is the number of candidate models), which is "not sensible"...AICc tends to have practical/performance advantages over BIC...AIC is asymptotically optimal...BIC is not asymptotically optimal...the rate at which AIC converges to the optimum is...the best possible.
In the AIC talk section, there are numerous comments about the biased presentation of the comparison with BIC section. One frustrated contributor protested that the whole article "reads like a commercial for cigarettes."
In other sources, for example this thesis appendix the tenor of the claims for AIC seem more realistic. Thus, as a service to the community, we ask:
Q: Are there circumstances in which BIC is useful and AIC is not?