But neither are correct, as the following URL explains:
http://europeanhistory.about.com/od/catherinethegreat/a/hist myths1.htm
In brief, the horse myth arose because to insult someone female, invoking their sexuality was considered to be especially belittling. The toilet myth arose because according to a biography, Catherine was discovered lying on the floor of a 'closet' adjacent to her bedroom. It may well have been a toilet - it's hardly an unusual place to die - but in fact Catherine's servants put her back in her bed. It was there she later died.