I have not really explored the other major incense manufacturers much but one of the things I liked about the Baieido sticks I have burned is the seeming reliance strictly on raw raw materials - as far as I can tell there are no extracts, isolates, or aromachemicals and the profile is very much just of a simple mixture of herbs and resins (I think the old US representative said this traces back to some degree to their roots as a provider of medicinal herbs?)
I find the scent is a little rustic or medicinal compared to Shoyeido (for example) which often seem to have a more complex naturally perfumed smell - like they have some kind of natural isolate or extract in them.