Hi flanello, thanks for your reply.
Yes, the radiation efficiency in CST and ADS describe the same thing. In CST, I take the radiation efficiency from farfield monitor which describes [maximum gain(ieee)/directivity]. In ADS, I take it by calculating maximum gain/directivity shown in antenna radiation parameters. I am sure that the impedance mismatch is not included in radiation efficiency since there is also a parameter called "total efficiency" in CST which includes impedance mismatch.
I have also compared the directivity. The directivity from CST and ADS are not so much different, but the big gap comes from the gain. And I have no clue why the gain is so different.
Below is a screenshot showing gain, directivity, and radiation efficiency from CST and ADS for the model I attached in my post above.
View attachment 99955