From the feedback...
When I upload a picture of The Bronx and start typing a category of "the bro..." the selector offers "The bronze..." but not "The Bronx..." presumably because I didn't capitalize the place name. Other programs with autocompletion don't mind whether we use caps or not and this one also should offer both upper and lower case completions. [[User:Jim.henderson|Jim.henderson]]
There does not seem to be any option for the builtin 'query' API to treat the query as case-insensitive.
The Commons search box uses the OpenSearch API (from Extension:OpenSearch) which seems to be case insensitive by default. It is possible to limit an opensearch query to a particular namespace, so this could be used with the category suggest. The result format is slightly different though.