You will need to be more specific. This is a somewhat subjective subject. To the man on the ground (or air...or sea) theirs was the worst. Worse in what way, casualties, ground lost, one side losing more of either than the other?
The SS City of Rayville struck a German mine and sank on November 9, 1940, with one of her crew killed. The SS Charles Pratt was sunk by U-68 on December 21, 1940, with two crewmembers killed.
USS Niblack (DD-424) dropped depth charges on a sonar contact presumed to be a submarine on 10 April 1941 USS Kearny (DD-432) was torpedoed by U-568 on 17 October 1941 USS Reuben James (DD-245) was torpedoed and sunk by U-552 on 31 October 1941
There was also a US pilot on the Catalina that spotted Bismarck and a USCG cutter got mixed up in that as well (but wasn't engaged). A lot depends on what you consider a "fight" as well. A USN ship following a German one broadcasting in the clear certainly isn't a friendly act when there are British warships in the area.