In the tradition of writing lazy reviews which you have probably gotten used to over the last year, I think I will combine these two movies into one review.
If you like teens hunting each other or pirates hunting down giant freighter ships, then either of these movies will do for you.
If you like elite green beret teams using night vision goggles to take out kidnappers, then I recommend Captain Phillips.
If you like movies about unjust governments abusing their citizens and youngsters rising up to stick it to the man then you will probably like Hunger Games more.
If you like Tom Hanks speaking like a Kennedy for the first half of a movie then you will like Captain Phillips.
If you think Phillip Seymour Hoffman is a great actor, but has some crazy long eyebrows (not being critical, mine are starting to do the same thing), then Hunger Games is for you.
If you can't get enough of Stanley Tucci's over the top portrayal of the equivalent of a futuristic Entertainment Tonight Host, then Hunger Games it is.
If you like hearing a scrawny Somali thug repeat himself by saying things like "look at me, look at me.." or : maybe in America, Maybe in America" Then go for Captain Phillips.
If you like WWE when they have a battle royale, then you will probably like Hunger Games since it is kind of the same thing with 24 participants going after each other in the square circle so to speak.
Either way you can't go wrong. Both of these movies were really good. I give Captain Phillips 8.1 and Hunger Games: Breaking Bad 8.0 stars. And yes, I can give stars. I may not be a professional critic but I've been doing this for over 5 years now.