Corrections in red.  Stylistics in blue.

Fewer accidents are caused by traffic jams than by drunk [1] drivers

There are so many accidents that are caused by traffic jams in the big cities.
The Drivers are required to be careful and react quickly on the busy roads.
Even law-abiding drivers sometimes get into trouble because of lack of distance between vehicles. 
But during the rush-hour driving, a driver is ready for the dangers of the traffic, and knows how to cope with it.  However, a drunk driver increases the threat to the others, increasingly because the latter don't expect the danger and can't manage it.
That is the reason why a drunk driver is/represents a greater danger on the road, and why he is the cause of many terrible accidents.

[1]  In slang, the word "pickled" can mean "drunk."  However, "pickled" is a very informal, and sounds much too frivolous [unserious] in a conversation about death and injury caused by automobile accidents.  In the context of automobile accidents, use the word "drunk."