Both options fit small homes, but they feel very different in use. Bands win on portability; dumbbells win on measurable loading and familiar movement patterns.
Storage and setup
Bands disappear into a drawer and travel easily. Dumbbells need a dedicated floor spot but require less anchoring and setup between exercises.
Progression
Dumbbell numbers make progress simple to track. Bands change resistance through the range of motion, so progression depends on band tension, grip, and positioning.
The practical answer
If budget and storage are extremely tight, begin with bands. If consistent strength progress is the priority, adjustable dumbbells make a stronger long-term foundation.