(A) Ammeter $A_{1}$ will show a higher reading.
Resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A_{c}}$,where $\rho$ is resistivity,$l$ is length,and $A_{c}$ is the cross-sectional area.
Since wires $A$ and $B$ are of the same material and length,$\rho$ and $l$ are constant.
Therefore,$R \propto \frac{1}{A_{c}}$.
Since wire $A$ is thicker than wire $B$,it has a larger cross-sectional area $(A_{c})$,which means it has lower resistance.
According to Ohm's law,$I = \frac{V}{R}$. Since both wires are connected in parallel,the potential difference $V$ across them is the same.
Because wire $A$ has lower resistance,the current $I$ flowing through it will be higher.
Thus,ammeter $A_{1}$ will show a higher reading.