There are two major factors here:
- How fast/often you can defeat the boss
- How much %inc. Item Rarity do you have, when you kill the boss
2 of 4 Items of every MoF Boss are affected by %inc. Item Rarity (For Spirits Of Fire it’s the Amulet and the Unique Idol)
The 2H Mace and Relic are unaffected, since they are a 50/50 guaranteed drop (one of them will drop 100%)
With some cleaver planning you can give yourself an enormous if %inc. item rarity, without making the boss actually that much harder, but if your build can handle it it doesn’t even matter anyway.
Logi’s Hunger is not an empowered only drop, so you might consider farming him on Normal, if your build struggles on Empowered.
This is already almost the case essentially, not quite cut in half, but if you go far away from the center and develop a good echo web, you already need like 20-40% less echoes, compared to a fresh echo web, if you keep the echo web developed.
Since deeper echoes give way more timeline stability.
You can reduce the amount of echoes needed to complete by even more, up to 50-66% if you push corruption.
Depending on the timeline and what route/strategy you are going you needroughly 25-30 echoes, when you start fresh on Empowered Monolith.
By pushing Corruption you can get to 10-15 echoes needed to unlock the boss, while simultaneously increasing your chance to drop the more rare items (the chance is increased by %inc. item rarity)
Shortterm, doing a few Shades will only help you kill the boss once or twice very fast, but long terms killing shades does help tremendously.
It does slow your boss kills down a little bit, because the echo web alwas resets and you need to re-discover it, but in the long term having echoes that essentially give you more than double the amount of timeline stability is totally worth it, especially in conjunction with having more %inc. Item Rarity, which boosts you chances in getting the rare Boss Drops.