The Darkroom Cookbook and/or The Film Developing Cookbook indicate that sodium thio. may not adequately fix modern emulsions so ammonium thio is the way to go. Also, over-fixing in sodium thio will start to bleach the image - ammonium doesn't have these problems. The value of short wash times without the additional HCA bath cannot be over-estimated either! The less 'tedious' work in the darkroom leaves more time for image-making.
All thiosulfates bleach the silver image to a certain extent, but the rate is higher on the acid side than on the alkaline side.
Alkaline fixers tend to keep better than acid fixers.