It depends on a number of variables.
One factor is the temperature difference between two air masses.
The warm air will hold more water than cold air, so if a warm front hits a very cold air mass the cold air will cool the warm air and it will become oversaturated with water vapor.
The more the warm air is cooled the more rain will fall.
Another factor is the way the air masses are moving. If a warm front moves over cold air slowly it will form a gradual transition with the cold air remaining near the ground and the warm air climbing gradually over it.
This will produce a prolonged period of rain. If a cold front pushes under a warm air mass it may form a much steeper boundary area between the two air masses.
This can produce very hard short periods of rain.