As described in Wikipedia, the honorific His Holiness is the official style used to refer to male leaders and highly respected spiritual figures of some religious groups. So, if you look at it in the Buddhist community, just to quote afew examples, the title His Holiness is given to great Lamas like His Holiness the 14th Dalai Lama, Tenzin Gyatso, His Holiness the Panchen Lama, His Holiness the 41st Sakya Trizin, Ngawang Kunga Tegchen Palbar Samphel Wanggi Gyalpo, His Holiness the 17th Karmapa, Trinley Thaye Dorje, His Holiness the 17th Karmapa, Ogyen Trinley Dorje, etc.
Traditionally, His Eminence is a style of reference for high nobility, still in use in various religious contexts. So I think it is a rank lower than His Holiness. However, I agree with you whole heartedly that there really is no "difference" because if we understand or realize that they have the qualities that we lack and would like to have, no words, titles or honorifics can substitute for the respect, humility and reverence we show outwardly towards them.