Sheik and Rosalina are the best characters in the game with or without customs. Pikachu is right behind them with customs, though he might be surpassed by Luigi without them.
Sheik and Rosalina don't necessarily drastically get better with customs, they are just THAT good conceptually that none of the other characters end up hard countering them suddenly or anything when customs are on. However, some of their customs fix some MUs they have that are otherwise a little troublesome compared to the norm. For example, Rosalina VS Shulk would be a fairly even MU without customs, which breaks the trend of Rosalina normally having a significant if not dominating advantage against most of the cast. With customs though, even the Shulk MU becomes fairly easy for Rosalina, as the Luma Warp, Guardian Luma, and Shooting Star Bit customs fix all of the issues she normally has against Shulk (the fact that not even she can power through the Monado's range, and the fact that Luma really can't be sent out much as Shulk will just jump into Luma with the Monado - the listed customs however, give Rosalina a Falco laser-esque projectile that's fairly quick, a way for Luma to pass through Shulk or appear on top of Shulk with little end lag, and a way to make Luma momentarily invincible which can also shield Rosalina. None of Shulk's customs give him any fundamentally different tools either, and are honestly not that amazing, so he gets nothing to give Rosalina new problems or anything).
If you're talking equipment, well, it doesn't matter who you play as. Just make a good build and you're set. Auto Heal x3 is pretty broken.