Quick answer: The best covered litter boxes combine a tight-fitting hood, a carbon filter at the vent, a wide enough opening for cat comfort, and a smooth interior that's easy to clean.
Covering the box contains ammonia and odors within the enclosure, slowing their spread. The best designs funnel air through a carbon or charcoal filter before releasing it. Replace filters every 1-2 months — filters that are saturated no longer absorb odor and the box will smell as bad as an open one.
Very small or very tall hoods trap more odor but make cats uncomfortable. Cats that feel cramped inside will stop using the box. The interior height should allow your largest cat to stand, turn around, and dig comfortably. When in doubt, go larger.
Top-entry boxes offer maximum odor containment and reduce litter scatter since cats jump in rather than walk in. Front-entry is more accessible and works for all cats. Elderly, arthritic, or overweight cats may struggle with top-entry — front entry is safer for these cats.
For odor control without an automatic box, a covered box with a carbon filter is the most effective passive solution. Cat comfort determines whether it actually gets used.