If both gauges are cylindrical, made of a durable, nonflexible material, and have a sharp-edged rim, the catch should be the same within a few percent, provided that the rain falls when the wind is light. In windy conditions, wind-tunnel experiments have demonstrated that the gauge itself distorts the flow in such a way that small drops that would otherwise land in the gauge are swept over the top, resulting in undermeasurement. Your question relates only to comparing measurements from two different rain gauges. Of greater interest is the absolute accuracy of measurement. For simplicity, we'll consider only nonrecording rain gauges with no moving parts.
Exposure is critical.
The gauges should be mounted with their openings strictly horizontal. They should be exposed well away from higher objects to minimize the chance that precipitation will be intercepted before it reaches the gauge. The height of the gauge above the ground should be low enough to minimize the effects of wind yet high enough to avoid the effects of splashing. The latter can lead to overestimation of precipitation. If the gauge has a funnel that directs intercepted rainfall into an inside tube, the funnel should slope steeply toward the center to minimize raindrops splashing over the sides of the gauge.