Plastic is lighter, and keeps oxygen out well enough for several months.
If you plan to age your beer for more extended periods you will need glass.
You should also be aware of some of the horror stories regarding injuries from broken glass. If you go with glass use all caution. I don't use my one glass fermenter very often, but others on the forum swear by it.
For 95% of homebrew scenarios the choice comes down to personal preference.
BTW, "neither" is also a viable option; that is not doing secondary at all.