There are two issues.

First of all, you need to match the reach to what you need. Brakes come in ranges, ie 39-49mm (often stamped on the back of the arm), corresponding to the vertical distance from the center of the brake hole to the center of the rim's brake surface. This is critical, though not to the last mm unless you're at the extreme end of the range.

Second, side pull brakes come in 2 basic designs, single pivot (both arms pivot on the center bolt) or dual pivot where the arms are linked to each other, but each is on it's own pivot. This matters because there's a difference if leverage and cable response. Replacing a single pivot brake with a dual pivot may create a situation where your lever lacks sufficient throw.

Seco