Which gives more accurate test results when testing for chlamydia: the urine sample or the cervical swab?

Both. The PCR technique used for both is very sensitive for even very small amounts of chlamydia. If a urine is obtained, don't do a midstream "clean-catch" like you would to test for a bladder infection. Collect the first part of the urine stream and don't use a wipe first.
Both good. Both are reasonably good tests. The urine sample has the advantage of allowing patients to get checked without subjecting themselves to a pelvic exam which deters some people.