I'm a bit out of touch, but of all schools in Sweden, the only I'd call elite - by the common meaning of the word - is Operahögskolan (I think it's called, the Opera school) and possibly Stockholm School of Economics and the medical schools of the larger older universities + Karolinska. Those places are highly competitive.
Everyone I know, from the little village I grew up in Sweden, who wanted to go to KTH, did so.