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Since 2.8.1, the bow has changed a bit. Dark divinity, Dark Projectiles, adds +125% souls (2.25x), Stones of Activity no longer has a cap on bow souls and can provide an even greater multiplier now, and Enhanced Soul Grabber adds +20% souls (1.2x), so I feel like making a new calculation for 3.0.1.
1.5 (SG) * 1.25 (ASG) * 2 (WW) * 2.25 (DP) * 1.2 (ESG) = 10.125x soul multiplier without the Stone of Activity. I don't know the best way to calculate the stone, so I'll just use my current level 16 stone of +187% souls (2.87x) for the rest of this post. 10.125 * 2.87 = 29.05875x soul multiplier when killing with the bow. But wait, you can also boost kill (2x, 3x if augmented) with the bow, so my actual soul multiplier with the bow is 87.17625x when boosting.
The new Rage upgrade provides a 100x soul multiplier for every kill, so right away it looks like it is better than the bow. AFAIK, the multiplier can be added to by three different upgrades: +10x from a cheap ascension upgrade, +10x from a quest upgrade, and +50x from an expensive ascension upgrade. Since I haven't completed the quest yet, my multiplier is 110x and I'll use that value for my comparison. Despite Rage mode causing your character to move fast, it does not benefit from the boost kill upgrade, which is why it was included in the bow calculation.
Both are able to crit, and both are multiplied by the soul bonus event from a random box, so those values don't need to be applied.
My Rage is about 26% (110/87ish) better than my bow, but it is probably better to save that Rage for a mega-horde where I can't use the boosted bow effectively. Spamming Rage when it is available isn't really worth it. You cannot Rage into a chest hunt
Edit: I completed the quest, so my Rage is now 120x. It is about 37.7% better than my boosted bow now. The expensive ascension upgrade, for a total of 170x, would make it 95%, almost double the boosted bow. I doubt I'll see that anytime soon. I'd likely Ultra Ascend before that happens, which would give me a better bow multiplier.