But in certain circumstances, a cloak of elvenkind will make it easier to hide than invisibility will. I can't explain that. Why wouldn't invisibility also grant you an advantage?
It does better than mere advantage or disadvantage, but that applicable information is spread out across multiple locations in the Player's Handbook (PHB), not in the "Invisibility" spell.
Location 1: In Chapter 7 ("Using Ability Scores"), there is a
sidebar on "Hiding," and the second sentence within the third paragraph says: "An invisible creature can't be seen, so it can always try to hide."
Location 2: In Chapter 8 ("Adventuring"), under the minor heading "Vision and Light," the nature of an "obscured" area is given as:
"A given area might be lightly or heavily obscured. In a
lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
A
heavily obscured area--such as darkness, opaque fog, or dense foliage--blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see appendix A)."
[PH Errata: A heavily obscured area doesn't blind you, but you are effectively blinded when you try to see something obscured by it.]
Location 3: In Appendix A ("Conditions"), the entry for the "Blinded" condition says in its first bullet point, "A blinded creature can't see and automatically fails any ability check that requires sight."
Location 4: Also in Appendix A ("Conditions"), the entry for the "Invisible" condition says, "An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. . . ." That's in the first bullet-point. Then, in the second bullet point, it goes on to say, "Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage."
Putting all of those together:
• When you're invisible, you can always try to hide (from sidebar on hiding in Chapter 7).
• When you're invisible, you're heavily obscured for the purposes of hiding (from the entry for "Invisible" in Appendix A).
• When you're invisible, any creature trying to see you is effectively blinded with regard to seeing you (from the PH errata about "Vision and Light" in Chapter 8 about observers being "effectively blinded" when trying to notice something heavily obscured).
• A creature that is effectively blinded "automatically fails any ability check that requires sight," per the "Blinded" condition in Appendix A.
Therefore, when you're invisible and making no noise -- and not knocking things over or pushing branches aside, which an observer
would notice -- tnen all observers automatically fail their passive perception checks to detect you when you're trying to hide. That's a lot
more effective at hiding than merely having advantage or a roll, or their having disadvantage on their check.