Disintegrator shredders provide the highest level of security since the paper is reduced to tiny pieces or even powder, but they are very expensive for home use and are not usually necessary for household security.
A shredder makes disposal of paper documents easier - since paper shreds are more compact than crumpled paper, fewer bag changes are needed.
Confetti-cut shredders, or cross-cut shredders, cut the paper bot horizontally and vertically, making very small fragments.