Both are good companies.
It depends on what you want to do in life. If you are actually offered employment with both, then base your decision on what fits best with you. Both airlines have an international cargo operation. Fed Ex also has a large US domestic overnight package delivery operation. Cathay has a large international passenger operation. With Fed Ex you will be based in the US (unless you bid Subic) with Cathay you can be based in the US but your career will be far better if you want to go to Hong Kong, and you could also bid for other bases in the world if you have the right of abode.
So decide what you want, passenger or always freight? Do you want to live in Memphis or Hong Kong (or commute)? Are you interested in new cultures and people, or is a ride on a NYC subway enough for you? If you go to Fed Ex it will be easy to fit in as an American. If you go to Cathay you will have to adapt to a slightly different culture.
If you are actually lucky enough to have an offer from both, decide carefully and include your family in the decision. If you are looking for work, apply at both, as getting hired at either isn't as simple as sending in an application.