For strength, generally, they do not compare. Generally, the muriatic you by at the hardware store is ~32% and Nitric is generally ~68%. However, each can be diluted with water to make weaker solutions.
Both react differently with respect to organic material, which is why the mention of muriatic as a stain carrier caught me unaware. As well, the reaction to iron is different for each acid.
Both these acids, as well as sulphuric, were well known at the time that Nitric was used to stain maple gun stocks. The fact that Nitric was the acid of choice leaves me believing it is the better choice. Sulphuric was sometimes added to the nitric to darken the wood with less heat.