Fixed Effects AIC

I am comparing a mixed model with a fixed effects model and using the Akaike Information Criteria to assist with the model selection. The basic AIC data follows:

Model Mixed Fixed Effects
Log likelyhood -19654.18 -18385.06
Rank of VCE 11 5
AIC 39330.36 36780.12

This suggests the fixed effects model is the better choice. However, when I include the number of group coefficients, 1522 less 1 for the constant, or 1521, the fixed effects
model has an AIC of 39822.12 = -2*-18385.06+2*(5+1521). Including the group constants suggests mixed is the better choice. By ignoring the fixed effects assumption of
individual constants for each group, is Stata reporting a misleading AIC and BIC?

Thanks