On average, how did the pulling power of oxen compare, in Civil War
days more or less, with mules ?

This site says that oxen are stronger that mules and horses:

http://ourworld.compuserve.com/homepages/trailofthe49ers/team.htm

This one is off the subject, but maybe of interest to you for Civil
War procurement:

http://www.eh.net/Clio/Conferences/ASSA/Jan_94/Kauffman

This is an index to an offline source that has an article:
oxen vs horses vs mules.  Scroll down to oxen to find it:

http://www.eaiainfo.org/csubl_r.htm

This site (p.39) also says that oxen are stronger than the same number of mules:

http://www.kancoll.org/books/gregg/gr_ch02_1.htm

Sorry, I could not find anything more specific.  One site seemed to
indicate that 6 mules or 6 oxen per wagon were used in the West.  And
another confirmed that military wagons were loaded with 3000 lbs.

myoarin-ga,
     If I have the power to do so, I declare your effort to be an
answer. So I authorize you to post it as such.

HOse7,
I am very pleased that my comment was a help.  Only GA Researchers,
whose names appear in blue, can post official answers (see the FAQs). 
You may close a question at any time (unless it is "locked" by a
Researcher).
Regards, and good luck with whatever you are working on,
Myoarin

For starters... it can be said that mules, oxen/bullocks,horses etc
are not pulling a wagon - they're pushing into the wooden frame that's
 fixed to the front of said wagon.

 Some zoologist nit-picker will probably challenge what I'm about to
say, but see if this answers your question.   With most, if not all,
4-legged animals, the front legs are there to hold it's front end off
the ground.   The back legs do all the pushing work.  A 1000kg bullock
leaning into the yoke, must have more effect than a 500kg mule.   A
major problem with bullocks is their speed,  about a slow walking pace
for a human,  which isn't much fun if General Jubilation T Cornpone
wanted to move supplies from A to B in a hurry.

pademellon, my question was probably not specific enough, but I want
some kind of equivalence, like two oxen can pull a weight that
requires x number of mules. I already knew that two oxen can pull more
than two mules.

Pademellon-ga has a point; oxen's greater weight and lower center of
gravity give them better 4-hoof traction, perhaps significantly better
when the going gets rough and a mule or horse cannot really apply its
front legs.
I don't remember if it was in a site I posted, but one mentioned the
comparison of two contractors for delivering grain or something, the
one with two teams of horses, the other with a team of horses and a
yoke of oxen.  The latter was faster delivering in the wet weather
with muddy roads, but the other faster on returning empty.  Somewhere
else, ox teams were said to average 2 miles per hour, horse and mules,
5 mph.