Would AGM/FLA have a lower efficiency using this measurement?
Yes because they:
i. have a much higher self discharge rate than LiFePO₄,
ii. need to have a float charge applied, which, while a low current, still adds up as it needs many hours, and
iii. there's much greater voltage difference between charging and discharging
On that latter point note there is a difference between coulombic efficiency and energy efficiency.
Most of us are quoting energy in / energy out (which is correct for energy efficiency) but you can also measure coulombic efficiency, i.e. coulombs in / coulombs out. For lead acid coulombic efficiency is generally significantly higher than energy efficiency due to larger voltage difference between charge and discharge than occurs with LiFePO₄.
e.g. with lead acid you might have 85% coulombic efficiency and 70% energy efficiency, although actual numbers will vary depending on depth of discharge and how the batteries are treated. For LiFePO₄ both numbers are going to be in the 90+% range, often high 90s because of the modest cycle depth in many applications.