IMO, I find both amps into 4ohms to be as loud or louder on a gig at 4ohms than the iAmp800. However (as you know), I don't think the iAmp's wattage is 'phony', but rather that huge deep bass extension results in a lot of wattage from the iAmp going to reproducing those very low frequencies. That was always my frustration with the iAmp. Even though the bass control is semi-parametric, it is still shelving (at least that's what my ears told me)... so moving the shelving point up to boost the upper bass for punch still boosted the rest of the low end, and cutting low end at a very low level left a hole to my ear in the low mids, even with the low mid semi-parametric set to the wide Q level and boosted at the upper bass level.
So, another one of my long winded answers

... the F1 and LMII have more 'perceived volume' to me into 4ohms on a gig than the 800, but that's primarily due to a more attenuated low end, and a warmer, punchier, wider more pleasant mid response versus the iAmp.. Both are honestly rated but voiced very differently IMO and IME.
The SD800 BURIES the iAmp in volume IMO, but unfortunately seems to have a similar issue with super deep low end extension.. massive low end wump.. massive rumble, but actually not as much punch as the smaller amps to my ear. The SD800 would be more of a 'direct competitor' tonewise to the iAmp800, in a louder, smaller, and much lighter package IMO... a little bit clinical in the upper mids and treble, and huge, wide, massive low end.
I dig the 800 a lot, but if I was forced to choose between it and the LMII, I'd keep the LMII.