Web developer sort of implies a jack of all trades, but master of none. It sounds 90s because it's very similar to Webmaster which now has a bad rep for the same reason. Keep in mind that the 90s was an era where you could know everything, and that just doesn't exist anymore in one person.
Front end developer is nicer because it implies that you're a specialist and can work as part of a larger team. Also the web is so much more complex than it was in the 90s due to the number of things you need to know well and the wide range of browsers and platforms that are available.