I've owned all three. The PRIMARY difference is tone, with the SD800/LMTube800 having a wider low end, less low mid push (even when EQ'd), MUCH more aggressive upper mids, and a more 'clinical' top end to my ear.
While the volume of the LMTube800/SD800 is a bit more than the LMII, the TONE profile (i.e., less punchy) results in the increased power of the 800 series to not really seem louder than the LMII (I have not played the III) in a mix on the gig.
Again, if you think that the LMTube800 or LM800 are 'louder' LMII's or III's, IMO and IME you will be disappointed, given that they sound so different, and the volume difference is not night and day. IMO and IME!