Choosing a ball for Drowzee? Compare the normal and shiny recommendations below with their reference sprites. “Best” here means a colour or theme match, not improved catch odds.
The community colour-match recommendations for Drowzee are Ultra Ball.
The community colour-match recommendations for shiny Drowzee are Dream Ball, Love Ball, Heal Ball.
Choose the appearance you prefer from the listed options. Normal and shiny Drowzee can suit different balls; these are community suggestions, not a measured ranking.
Source: Legal Matching Pokéballs 2.1 by OracleLink. Community recommendations, not a per-game legality checker. Availability depends on the game, form and encounter.