There seems to be some confusion over the distinction between resolution and accuracy. Resolution is the finest increment that you are able to resolve. i.e., a spin indexer with 360 discrete positions has a one degree resolution. There is no way that you can set a 15.5º angle. However, a 15º angle would be 15º +/-4' (.07º) from the Shars spin indexer specification.
The biggest difference between an indexer and a rotary table is that the rotary table allows moving to any angle within the limits of the RT resolution. An indexer has to work with the available divisions. It works well in making bolt circles with a set number of holes. You cannot set a 13º57'23" angle with it
OTOH, my RT has a 90:1 gearing and is able to resolve 5" (.0013º). If I wanted to make a 127 tooth gear with the RT, I could by incrementing my position by 2º50'5". (To minimize errors and prevent error stacking, I would use an Excel spreadsheet to calculate the settings). It would be more cumbersome than using an indexer but it will get the job done.
In an ideal world, I would have both but faced with the choice of an indexer or an RT, my choice would be the RT, simply because it is more versatile.