This is not about pros and cons, this is how the matchup should be played. Both of my best friends play Rosa and I play against her all the time so I know what I'm talking about.
The most important things for Rosalina in this matchup are maintaining control over the center of the stage and keeping Luma alive. Both of those things are crucial.
For the first thing you have to know your opponent and know yourself. Sheik has only one way to approach Rosa that is f-air. You have to remember this, normally you shouldn't get grabbed, and if you do Luma should always interrupt the followup using an aerial (u-air most of the times). Sheik shouldn't be able at all to follow a f-throw or a f-air with bouncing fish, which is bad for us Sheiks, because bouncing fish is our most damaging combo follower. We need to connect 4 f-airs to do the same damage as f-throw to bouncing fish so remember this. Having said this, you know how Sheik is going to approach.
When people get defensive, we Sheiks like to charge needles because players get offensive when they see us charging needles. Don't fall for that trick, if you are far away from Sheik you can't punish the charge.
Getting offstage is the worst possible scenario for Rosa so you should try to be in the center of the stage, especially at higher percents. If you get Sheik offstage don't be too greedy edgeguarding, you can die if you go offstage to edgeguard her and most of the times it's not worth it. It's better to wait Sheik near the edge and kill her with a smash attack, as Sheik dies pretty early and Rosa doesn't have much trouble killing her.
If Luma dies you are at a great disadvantage and a good Sheik will try to maximize the advantage. You are now susceptible to a lot of damaging combos and kill setups that you should be safe when Luma is alive. I don't know how it is in other matchups but here it's like the matchup is even if Luma is alive but if she's not is like -2. You have to be really careful when this happens, as you can eat 45% damage from a single combo at low percents and at higher percents you can die way more easy than with Luma. If you maintain Luma alive you should live until 170%.
Most Sheiks have a bad habit of being overagressive if they are the first to lose the stock. Watch out for this, if it happens you can do a lot of damage to Sheik punishing stupid things, like anything that's not f-air.
The stages I like to go against Rosalina are Lylat Cruise and Castle Siege. Lylat Cruise is a good stage for Rosa in general (in my opinion) but the stage tilting helps Sheik's edgeguarding a lot, opens up new possibilities for kill setups to Sheik (like d-tilt at the edge to u-air, kills like 120-130% depending on rage) and Sheik can tipper u-smash you if you are on a platform and you can die like in 90%. Castle Siege is great for us in every transformation, the first is small so we can throw Rosa and Luma offstage easier, the second one allows us to kill with f-air strings off the walkoffs and the third is the same as Lylat. You should avoid this stages.
The best stages for Rosa in this matchup are Halberd, Delfino Plaza, Town and City and Dream Land. You can kill pretty early in Halberd because of the low ceiling and Sheik can't take advantage from the shape of the stage. Delfino is great against Sheik, in the transformations I died as early as 0% with an u-air near the top and Sheik can't benefit at all in the transformations (maybe except the one with the parasols). In both of this stages we can't stage spike you and we can't bouncing fish into the stage, so our edgeguarding game becomes worse. Town and City and Dream Land are similar in a way that both have a lower than normal ceiling and if you use the platforms correctly you can kill pretty early with an u-smash or u-air, even without Luma, but the same can be said about Sheik so be careful of high u-airs.
One of my friends like Duck Hunt but I find it really good for Sheik, maybe the best stage against Rosa after Castle Siege and Lylat. The tree and the bush helps our edgeguarding game if you try to recover high and we can cling to the walls if you try to recover low. I don't find good things about the stage for Rosa maybe except for the left tree that can aid you going higher for an u-air.
I find Final Destination, Battlefield and Smashville to be slightly in Sheik's favor, as both characters can benefit from these stages but I think that Sheik does better in those.
As my opinion for the matchup is -1 for Rosalina, like i said early, if Luma is alive the matchup is even but if it's not the matchup is like -2 for Rosa, as Sheik is fast, can capitalize Rosa being alone and her combo potential and kill power gets unleashed.
I hope I'm not forgetting anything, if you have any questions about the matchup ask me and I will try my best to help you guys.
