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Triangles $ABC$ and $DEF$ are similar. How much longer than segment $BC$ is segment $AB$?

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The corresponding parts of similar triangles must follow the same ratio. Since $\dfrac{DF}{AC}=\dfrac{20}{4}$, the larger triangle is 5 times the size of the smaller triangle.

Therefore,

$$AB-BC = \frac{29}{5}-\frac{21}{5}$$ $$= \boxed{\frac{8}{5}}$$