What program is best at JPEG compression?

Are some graphics programs better than others for compressing JPEG?
A friend swears that Image Ready is the best for getting the
smallest file with same quality.
But I see a few companies have made utilities purely for
compressing pictures, and claim they obtain better
compression than the top tier graphics programs.
I presume there are different numerical routines used by
different companies in their software, but I would guess
maybe 5% variation in file size at best.
I know there was a comparison done several years ago,
but the website with the pictures seems to be kaput.
(www.imagecompress.com ?)
Is there a recent comparison of different programs to see
who offers the best compression?
That is, best quality for same size, or smallest size
for same quality.