The yellow Sheikah symbol on her Melee Red costume and the purple Sheikah symbol on her Melee Green costume swapped places. And with it, they've swapped places on the Sheik Costume Tier List. Purple Sheikah symbol just isn't viable. That red scarf on PM Blue has shot it up on my list, though. Please nerf that style, I can't keep living this double life of cheating on my beloved Default costume anymore.
Actually though. But on the real:
Her play in Melee revolved around D-throw chains. It's PAL D-throw now, so now she has to mix it up with B-throw to mess with opponents' DI. Further, since she can't tech chase them out of her D-throw knockdown, she becomes a lot more oriented around quickly comboing and then hitting away to reset to neutral, as opposed to like.
RAR B-air is a great spacing tool. RAR (reverse aerial rush) is a tech introduced in Brawl, where a character is dashing, turns-around, and then immediately jumps in the direction they were running. This lets them jump backwards in the direction they were running in, without losing much momentum. SHFFLing RAR Bairs is pretty great.
She has crawl+wall cling now, for what it's worth. Not many people use those, but maybe you can find something out of them. Footstooling is a useful change for some characters with falling or spiking D-airs, but that doesn't really apply to Sheik.
Needles have lost their...can't remember the politically correct term for it, but they've lost a lot of the priority they used to have in Melee. By that, I mean her projectile doesn't immediately cancel out every other projectile in the game like fully-charged M2 shadow ball or Samus charged shot. So you'll have to actually shield or avoid those like every other character in the game now...welp.
In PM, if you sweetspot the ledge, even if you're facing backwards you can grab it. Because of this, you can Shino Stall onto the stage and hit an opponent with the explosion, teleport back to the edge (facing away from the stage), and still grab it. This isn't super well-known about in PM meta yet, so use it sparingly. But if you ever do get caught wanting to shino stall by ledge (if you're that kind of guy aha), doing a quick one on stage to surprise an opponent can really screw up their momentum.
Down-B has also gotten a significant buff. Try it out sometime; lookup some combo vids and kneel before thy old maker.