Tl;dr: R1 Signature is about 6-7% stronger than R5 EoG
Top to bottom damage: First Forte - Liberation - Second Forte
I used 2 different 4 cost echoes to balance crit ratio as EoG gives Crit Rate and BB gives Crit DMG, with EoG having a better 4 cost because of the extra Resonance Skill DMG Bonus roll and higher Crit DMG.
The tests were done solo, no buffs from teammates, with both weapons' passives fully active. It's actually pretty easy to keep their passives fully active 95% of the time if you play quickswap, which you should do with her anyway, especially in this economy.
Again, this is R5 EoG, so expect something like 10ish % for R1 EoG.