Best test for estimating hCG:
Before answering this questions, let us first understand what is bioassay, immunoassay and Radioimmunoassay

Bioassay – A Bioassay is a test that uses animals or live tissues to look for a response to the hormone that is injected.
Immunoassay – An Immunoassay is a test that uses antibodies detected against the hormone to “capture” the hormone. The test uses materials or substances that are related to or are a part of the immune system. To perform an immunoassay, cells are introduced from the immune system which may or may not have an antibody and cell clumping is observed.
Radioimmunoassay – An radioimmunoassay uses a radioisotope as the label to detect and measure the amount of hormone present in the sample.

Bioassay for detecting hCG was developed in 1930’s. wherein samples were injected in rabbits, frogs etc and ovulation was observed. These tests were expensive, slow and insensitive for hCG as they couldnot differentiate between LH and hCG.
Bioassay for hCG is an outdated test these days.
ELISA – It consists of immunosorbent assay of monocional antibodies to detect B-hCG. It forms the bases of home pregnancy tests. This is more sensitive and specific and can detect hCG in serum upto 1-2 mIU/ml. Radioimmunoassay and Radio receptor assay are more sensitive than ELISA and detect hCG Gupto .002 mLU/ml in serum (RIA) or .05 mLU/ml (IRMA)
But between the two, Radioimmunoassay is more specific as it doesnot cross react with luteinizing hormone and is the best test for detecting B-hCG
“Radioreceptor assays are more sensitive, but not much used as there is cross reactivity with LH.”
Radio immunoassay
ELISA
Radio receptor assay
Bioassay