Both used in fixer shall give you an alkaline fixer, Both will clear quicker than an acid fixer. Ammonium thio may give more odour. Sodium thio is used in TF2 where ammonium thio is used in TF3. Ilford ilfofix used ammonium thiosulphate, I use this for my salt prints and pryo negs without any issues.Most rapid fixers are acid based. Alkaline fixers seem to be a little more gentle.
Pat