Think about what you just said there. I mean, take it out of game terms... OF COURSE there is an advantage to being invisible if you're trying to sneak up on someone. If you're concealed behind a curtain, wait for the target to turn around and start reading at his desk, and sneak up behind him, that's a straight stealth check. If you're invisible, you'll have advantage because if you do make a slight noise and he glances over his shoulder, he won't see you and might think it was the wind.
Similarly, if you have crafted a disguise and are impersonating someone to get close to your target, you would roll a straight deception check. If you're wearing a magical illusion that makes you look exactly like someone, though, you'll have advantage on that roll.
That's part of the rule that says a DM can and should give advantage or disadvantage when it makes sense.
I am thinking both in
and out of game terms. This is not a "RAW" argument.
So, while I agree that this all comes down to the DM assessing the situation and assigning advantage and disadvantage where it makes sense, I disagree that it makes sense to say, generally, "someone who is invisible has advantage on stealth."
Take your example. Sneaking up on somebody across an open space (such as a room), is very difficult. This isn't a straight stealth check. Any number of things could go wrong. Generally speaking, to remain hidden, you need to be totally concealed
for the duration of your action, movement, or what have you. So being able to sneak across an open room is already depending on the person you're sneaking up on to not be looking around. Unless the person is very engrossed in what they're doing, I'd consider it definitely to be a disadvantage situation. If the person is engrossed in what they're doing, the resulting disadvantage to their perception would net out the disadvantage to your stealth, and I'd just do it as a straight check. If that person is distracted, and you have total cover (due to invisibility or any other means), you no longer have disadvantage, but they still do, so, under those circumstances, sure, advantage. But, again, the advantage comes not from your invisibility, but from the comparative lack of attentiveness to the other senses.
Generally speaking, total concealment is a prerequisite for hiding. It really doesn't matter how you get it.
If the circumstances warrant hiding without consistent total concealment, then invisibility will start tipping the scales of advantage and disadvantage. But I've seen a lot of table-top situations where folks have tried to argue that invisibility gives them advantage in doing things like sneaking down a hallway, or some other thing that would be impossible were they not invisible. That's all.
Ugg, sorry, missed my game two weeks in a row because of long work hours. Taking it out on arguing stupid rules crap on the internet.