It was fairly obvious early on one of the changes the relaunch would have was new Robin costumes. What changed and what stayed the same.
Eagle eyed readers of Red Hood and the Outlaws caught the easter egg of the scaly undies (pictured below) along with Dicks' past uniforms he had. But Nightwing #0 showed the new Robin look. The iconic clasps on his tunic are gone with the undies and the belt. He also has pieces taken from Tim Drakes' first Robin costume (pre-Flashpoint) such as the pocketed gloves and black/yellow cape. The mask is more Nightwing like with it's edges than the more traditional domino mask he used to sport. While the armored look is more pratical it's missing a few key elements. There's no where to put any tools he needs. Otherwise it's a look I don't mind.
In RHATO #6 Kori showed Jason a few of Dicks' former uniforms. It doesn't look like the fan favorite black and blue (with finger strips) costume ever existed. But Dick did have a look much like his first Nightwing costume (dubbed the discowing suit.) This blue and gold suit was worn at the start of his solo days while Jason wore his own Robin uniform. While there was never an explanation for the costume on the left of the discowing suit it's the one Jason currently uses. (Well at least the top.) There's a red bat on the center of the chest and smallers bats on each shoulder.
First seen in RHATO #3 this is the most armored look of the Robins. Sadly not many artists have done it justice since it was created. But here's some basics to remember to make it look different than the others. Jasons' mask isn't pointed like the other boys and it's red not black. He has a yellow cape, there's space between the shoulder pads and gloves. The helm of his top makes a "w" shape. While you can't see it in these pictures the clasps are pointed like Helena Waynes' except for the top with it designed to look like a bird.
Also note the side of his legs have what looks like birdarangs which look just like the clasp on the tunic. Basic elements that greatly differ his look from the others. Finally Jason has a costume of his own.
The second pre-Flashpoint Tim Drake costume is still in canon. This was also seen during the fight with Superboy when Kid Flash stole this costume. Tim has a pointed mask, his black/yellow cape, clasps, black gloves/boots, and a belt. Oh and the black undies. Weird to think that he's now the only Robin that had a costume with visible underwear. Yes I know about the Red Robin thing but if he still has Robin in the title he still is one.
This is basically the same as it was before the relaunch. They tried to make the cape more "feathered" like but from what I've seen it hasn't really stuck. Like Dick, and to a lesser extent Tim, his mask is the pointed Nightwing style. A basic black under suit covered by a more traditional pre-Flashback Robin tunic. I never saw the point in the boots being laced especially since he currently has them undone all the time. The gloves are shorter than usual and the cape has a hood which fits the character perfectly.
With the pointed clasps, space between the shoulder section/gloves and red mask this reminds me a little of the Jason Todd look. But she has a different twist on the armored costume with her shoulder pads, gloves, boots and knee pads. The "x" crossed belt is also used on her Huntress costume, it's a nod to her mothers' look on Earth 2. The black/yellow Tim Drake cape makes another appearance. It's a solid uniform even if I'm not too fond of the knee pads.