A perfect BotD in an Eth beserker axe does roughly 201-530 damage. it can potentially outdamage a grief. with mana and life leech, it opens up slots otherwise taken by these stats. it can reach max breakpoints for almost any weapon.
And it doesn’t require hunting down a 4s phaseblade, which can be a process in itself. It just needs a socket quest. It is a very solid (and expensive) RW, and is probably superior to Grief overall.
Death can’t reach as high as BotD, but has amazing crushing blow, life leech, and a nice AR boost. the Ctc is just icing and relevant depending on the build. It’s biggest limitation is no IAS, so harder to reach breakpoints.
Grief’s biggest advantage is it can contend with the top RW’s, but cheaper. Simple as that. it doesn’t have the leech on it, meaning you need it from other sources, but again: cheaper. most players will be able to eventually get Grief, but BotD is going to pretty much be the domain of whales/high end farmers due to Zod.
When deciding, you need to take into factor the areas that the rest of your gear is lacking. If rune aren’t an issue, then it’s really not a question: BotD is superior in its top end damage and stat distribution. BUT…grief is so much easier to obtain, and can do the job, so…