I remember seeing somewhere (possibly on this board) that opposed tests are massively weighted towards the side with even slightly higher stats. The person posting had a house rule that all opposed tests are made with a target number of 4, so the only difference is the number of dice. I was curious how true this was. So I decided to run a simulation.
I've got two orthogonal rule variations that I used - various target number calculations and a modified rule-of-six where every 6 above the target number counts as an extra success. I went up to 12 because I was interested, and didn't go above that because I wasn't. This isn't any fancy mathematical proof, it's just the result of doing 100,000 tries and checking the results. (Ties don't count, it just retries it.) That's why none of the identical-stat results are precisely 50%.
The target number options include standard opposed tests, target number of 4, and target number of 2 + opponent/2, which I added to see how well it worked. (Badly.)