I have used two methods for measuring my bodyfat %, using a body composition monitor which I step onto like a scale, and it reads about 20% fat, and I have skin caliphers that I use which is reads about 11 mm, which is roughly about 11-12% body fat. Which of these would be more accurate?

I've always found the scales to be WAY off.. calipers are great if you do enough sites. One or 2 sites and they aren't very accurate, but 7 or more sites and they become pretty damn good.

I mostly agree with that!
 
The methods WE can use to test our bodyfat ourselves are unreliable on a one time basis. 
They are better used to track changes over time on an ongoing basis. 
Test every 1-3 weeks depending on goals.

 
I compared many BF testing methods to see how they work with my body.
You can see there is a variance between methods. 
I can take any of the tests over and over and I get the same result.
I have been taking BF measuremnts for decades, so I am quite use to it.
 
Here are those test results ...
16.34% -Tape measure 3 location
14.5% - Tape measure 2 location
13.2% - Skin Fold 1 Location
19.4%  - Skin Fold 2 Location
9.4% - Skin Fold 3 Location
15.1%  - Skin Fold 4 Location
15.9% - Skin Fold 4 Location (actually an aggragate of multiple tests of: 4 folds-15.1%, 1 fold-13.2%, 2 folds-19.4%)
11.27% - Skin Fold 7 Location
16.6% - Bio-electrical Impedance
 
Wild isn't it.  But they are all based on various assumptions...so that is why it is better as a tool for tracking over time.  Pick a method, get good at it, and stick with it.
 
"This is the only low cost caliper accurate enough to be used for professional measurements and is the most widely used professional caliper in the world. Its primary disadvantage is that it does not look professional, high tech or sophisticated. It is easy to use with convenient pistol grip and trigger, and it is spring-loaded to insure consistent measurements. It is made of ABS plastic and is the most durable of all calipers. It has a 5 year warranty, the longest of any caliper. "

According to the second site, I took my body fat % from three sites, and it is roughly about 10% bodyfat. But, I think that the body fat composition monitor is off because it says 20%.

Like I said...it is really to be used to track CHANGES over time, not for a one time measurement!
 
Keep using the 3 point, if you ask me.  At least you can do it alone!
4, 7, and 9 take someone to measure on your back!
 
Though I do prefer the 7 or 9.
 
The scale is based on some crazy computation and not based on us heavily muscled folks.