In my mind that is not an easy question. As an example take Azo
contact speed paper. I contains silver chloride and nothing more.
Both sodium and ammonium thiosulfate will complex great amounts
of silver in the presence of chloride.
 Neither of the thiosulfates will complex more than a little
silver in the presence of iodide. Chloride/bromide mixed emulsions
fall between the two extrems.

 The hypocheck is an iodide check. It will give a "bad" reading at
very low levels of silver. To some extent it is a test of the fixer's
capacity for silver in the presence of iodide and that is very low.
 I did a test where the fix with a few drops of hypocheck tested bad
but, IIRC, forty drops of bromide "hypocheck" produced no turbidity
at all.
 The capacity of the fixer for silver in the presence of chloride
and bromide is much higher. Where there is chloride and bromide only,
I think a whole bunch of good fixer may be going down the drain.
 FWIW, Dr. M. J. Gudzinowicz does not think any hypo check worth
a damn. That helps a lot does'nt it. What do you think?             Dan

  They are not the same. In general, film is more tollerant
of small amounts of residual halide than paper. The reason
is the much finer grain of paper emulsions, especially warm
toned ones.
  Given that, IMHO, Hypocheck is probably not sensitive
enough for use with a single bath fixer for archival fixing.
The capacity of a single bath, especially for paper, is
extremely limited. Ilford gives 10 8x10 prints per GALLON as
the limit. For commercial standars, i.e., 20 year print
life, the capacity is much larger. For ecomonical fixing use
a two bath system. This has from four to ten times the
capacity of a single bath for either film or paper for
archival fixing. An Iodide test solution, like Hypocheck,
can be used for the first bath to determine when its at the
end of its life. Since the allowable silver content is much
greater for the first bath of a two bath system such a test
is reasonably reliable. Kodak has complete instructions for
using a two bath system in the _Kodak Black-and-White
Darkroom Dataguide_ and probably other sources. The use of a
sulfite wash aid, like Kodak Hypo Clearing Agent, following
fixing will also help to extend the life of the fixer
because it can remove some of the otherwise insoluble fixer
reaction products left by incomplete fixing.
  If the silver halide left over after development is not
removed pretty completely it will eventually decompose and
attack the image silver and also cause staining in the low
density areas. Really good fixing is as important as
thorough washing to film and print life.