This question began tripping up fans before "Fantastic Beasts" was released, since Newt's boat trip was teased in the trailers. Many people thought it would make more sense for him to either Apparate or use a Portkey.
Rowling's answer: "Apparition becomes increasingly risky over long distances. As with most magic, much depends on the skill of the spell-caster: Apparition requires knowledge of the terrain to which one is moving, or the ability to visualise it clearly. Cross-continental Apparition would almost certainly result in severe injury or death. Moreover, the beasts in Newt’s case had varying magical natures. Some could have Apparated with him, but others could not."
We assume the same answer applies for Portkeys, though she didn't specifically address this on her website.