I tend to agree with Karin and Wendy: comparing fitness bands and dumbbells is like comparing apples and oranges.
Both are good modes of training and can be used on clients (depending on their abilities and goals). Dumbbells, however, will not ‘snap back’ the way bands snap back because dumbbells rely more on gravity for resistance.
What you use really depends on what your client needs. Observe your clients goals and abilities then decide what works best.
Good answers. Both can provide potentially viable resistance overload to a specific muscle, muscles or muscle groups. I think that one key point to always keep in mind is that no matter what provides the resistance, the research suggests that in order to make significant gains in strength over time the resisted movement needs to take the target muscle(s) to temporary failure in 12-15 RM.