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Ampere's Circuital law doesn't include the boundary condition that B tends to zero as r tends to infinity. For an infinite current carrying wire Ampere's circuital law can have infinitely many solutions of B (also taking into care the fact that B is solenoidal field) out of which only one is permissible by taking the boundary condition.

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Neither Ampere's law nor Biot-Savart's law include anything about boundary condition for $\mathbf B$. In that respect they are the same.

But the Biot-Savart law is more general because it is valid even when the Ampere law isn't, such as when electric current is changing in time and $\mathbf E$ is still given by gradient of potential (induced field is negligible). This is the case, for example, for magnetic field inside plane parallel capacitor when being charged/discharged by time-dependent electric current.

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