If I have to choose between St. Patrick's Cathedral and Christ Church Cathedral because of time constraints, what would you recommend?
I would go to whichever one is closer to other places you'll already be, to save you travel time.
They're both very beautiful, with interesting artifacts and history. And they are both Anglican (vs. Roman Catholic) churches.
Enjoy!
St. Patrick's is bigger and surrounded by an attractive park. Christ Church is closer to other sights and its crypt is very interesting. For a tiebreaker, choose the one with Jonathan Swift's death mask (I forget which, but you can look it up).
We visited both. In Christ Church we did a bell-ringing class. Very tiring! Really liked the park setting around St Patrick's.