Dear Akifumi,
I am not sure what you mean by better performance. Is this with
respect to the final GAMMA-based scores of searches
under CAT and GAMMA respectively or do you refer to inference times.
Generally, CAT may perform better than GAMMA both with respect to
inference times (that should always be the case),
but may also produce trees with better scores.
In the latter case, CAT may yield trees with better scores under GAMMA
because the model is slightly different and hence, even when
using the same starting tree it may chose a different search path
through tree space.
For details please have a look at this paper:
http://wwwkramer.in.tum.de/exelixis/pubs/HICOMB2006.pdf
Alexis