When you are hidden or invisible, you get advantage on attack rolls because your target does not know where you are. If you break invisibility or move from being hidden, advantage is lost.

However, shouldn't the same apply to the Blink spell? On a success, you are not visible to anyone who cannot see into the Ethereal Plane, and could appear anywhere in a 25 ft. diameter (or more if no space is available) circle. I argue that if the FIRST thing you do out of Blink is attack (no movement, bonus actions, etc.) then you should have advantage on that attack.

Would this be game breaking? It takes a third level spell, so I think the cost is justifiable.

Blink says you appear right at the start of your turn.  Mechanically, that means you are visible and unhidden prior to making your attack, even if that is the first thing you do, so you don't get advantage.

a creature that is invisible has advantage on attacks, and invisibility granted by the invisibility spell ends when you make an attack, not prior.  So the first attack while invisible by that spell grants advantage, then the spell ends. 

the blink effect caused by the Blink spell ends at the start of your turn, prior to any attacks being made, so the advantage per the rules doesn't exist. Just because someone pops in to existence and swings a sword doesn't mean your reflexes and combat training fail.  It only does per the rules when said creature is still invisible when the attack is made.

The spell already grants very decent defensive ability: about half the time you are basically invulnerable until your next turn. Since you don't have to appear where you left you're pretty safe from melee readied attacks too. Enemies can ready aoe and ranged attacks but then they're using up both their actions and their reactions to do so, with opportunity, in case of spells, for concentration to be broken by your allies attacking them in meantime.

So to add advantage to your next attack is a little too much for a 3rd level spell. Which is why the spell doesn't grant it. And since it doesn't, no, you don't get the advantage.

With invisibility it breaks at the moment of the attack which is why the advantage applies. With Blink your turn starts, you appear, enemies can now see you, and it's "then" you make your attack, by which point it's too late to benefit from not being seen. 

If you want the advantage to attacks - get Greater Invisibility, a 4th level spell (which in and of itself indicates why you shouldn't get the same bonus as a 3rd level spell, especially since Blink's protective elements are stronger than Greater Invisibility's). 

EDIT: ninja'd by iconarising. 

Maybe it's just the style of player I am, but the unreliability of Blink is a huge downside for me. Like to the point that I won't waste a spell slot on it - maybe if it was 2nd level. I don't need to maybe disappear at the end of my turn - either I do or I don't. If I could reliably do so, I would do stuff on my turn that I wouldn't otherwise do. But since I can't count on it I need to plan every turn for the fairly likely case that I will not disappear, and thus end up playing pretty much the same.

It does have the advantage of defeating blindsight and tremorsense though, and I don't really think it needs a buff because you can roll lucky and be nearly untouchable. But honestly, I don't think it would break the game to have it work as OP wants. It's still not giving you reliable protection and advantage on every attack for the duration like GI does.