Can I separate user and system trace files in Oracle 11g?
I do not think that you can set the user and background dump destinations in 11g onward. One thing that might help is the TRACEFILE_IDENTIFIER parameter. I set this when I do a trace so that it is easy to find in the trace directory. 

For example I setup a trace like this:

alter session set max_dump_file_size = unlimited;
ALTER SESSION SET tracefile_identifier = 'bobbydurrett';
ALTER SESSION SET EVENTS '10053 trace name context forever, level 1';
ALTER SESSION SET EVENTS '10046 trace name context forever, level 8';


My trace file has my name "bobbydurrett" in it so it is easy to search for it.

Bobby