Be wary of common names (vernacular) many different plants have the same local name.
My experience tells me that the true and original 'burning bush' is Dictamnus alba' a perennial that when mature gives off a volatile oil. On a warm, calm summer evening the evaporation of this oil hangs around the plant and can easily be ignited.
You folks in the U.K. have strange plants. I prefer evergreen over deciduous so I vote of Nandina. But the plants are opposites so why would you be chosing between the two? One is dwarf the other standard.
It appears I did not understand your question. My answer was regarding plant nomenclature. Perhaps you could explain more fully what help you are seeking.
As Bullthistle said, 'Firepower' is a dwarf Nandina, with very colorful foliage that intensifies as cold weather sets in. It is 'evergreen' or 'everred'. It rarely exceeds 2 or 3 feet in height and spread, and I have never seen one bear fruit.
The typical burning bush is a euonymus, can get right large if you let it, has a blze of red in the fall and as mentioned before, drops its leaves. In some quarters it is considered invasive.
I think your choice is greatly dependent upon you application and the effect you want to exhibit.
pd, that is an interesting plant.... i shall have to investigate that further. Can you imagine the fun you can have with smokers who visit your garden with a plant like that.