On Final Fantasy XIV unlike the other previous Final Fantasy games you will be able to choose between 4 different languages for Voice Acting on Cut-scenes. This choice was suggested a lot by west players who wanted to be able to enjoy the cut-scenes in Japanese with English subtitles.
So in FFXIV it is possible, it isn’t perfect though, some characters speak in the background and it isn’t translated on the subtitles or the chat, so you will be missing some minor details.
As for the quality of the Voice Acting, a good voice actor can make a world of difference, but I’m unimpressed by the NA Voice Acting and I’m yet to hear most of the cut-scenes in Japanese, but they do sound better in my opinion.
But it isn’t nearly as bad as this (from Final Fantasy X):
If you are unsure what to choose, remember that you can always change the VA/subtitles and re-watch the cut-scenes in any Inn. That is also a good way to to see for yourself what kind of VA you like more.
In the end, most of you will keep the Voice Acting in English, but giving the choice to the players is an important move that I hope they follow from here on for future Final Fantasy Games (and Kingdom Hearts III, cof).