Chieftain > FAS. Fight me.
I would dare to even say:
Chieftain/Challenger > FAS
They both are very good ships, very similar. The difference is mostly weapon preference.
They both also turn much better than the Krait MK II. But they also share the drift with the Krait MK II. And as long as the OP doesn't describe his problems better, I would suspect that the Kraits drifty flight behavior might be a significant factor for his problems, which the Chieftain and Challenger also share.
All in all, I rate these ships to be awesome in the hands of a good pilot, but a hard uphill fight for a beginner.
Edit:
Also note that the Chieftain with it's rather unique hardpoint setup only really shines once you learned how to configure a ship. Many of the "good enough" setup you can do on other ships just don't really work there. So to really make the ship shine, you also need to have knowledge and experience in setting up ships and is not beginner friendly.