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OP, closed headphones have a lot of advantages but it depends on what you're using them for.
Closed headphones offer superior sound isolation compared to open-back headphones. This is good for you in that it rejects outside sound from your surroundings, and it's good for the people around you in that it seals the transducers so that you're effectively the only person hearing your music and the people around you (say, on the train or at the dinner table) don't have to hear whatever you're blasting. They also tend to be robust and rugged and will last a long time. If you're a studio musician, or a DJ, or a commuter, or just someone who wants a little goddamn privacy closed-back headphones are going to be great.
Now, open-back headphones are a little more wiley. Closed-back headphones don't offer any crosstalk (when you listen to speakers Left and Right BOTH go to both of your ears - which doesn't happen in closed-back headphones). Open-back headphones actually do allow for cross hearing from one ear to th other, PLUS MORE! Open-back headphones tend to have a much more realistic and distortion-free performance, better so-called "sound staging" because there are no weird unnatural reflections or resonances within a closed cup, which also results in a flatter frequency response.
IMHO though, for almost all situations I would recommend insert/in-ear-canal earphones, then closed-back, then open-back. But it depends, if you're just sitting in your living room wanting to hear beautiful tunes, open-back is the way to go for sure.
BTW, closed-back headphones are the headphone equivalent of /out/ for sure.
