Absolutely, in terms of sheer bang for your buck, LRM's are the best unit in the game. Period. Experimentation and spreadsheeting all confirm this conclusion. A skilled TEC with a good economic opener who can get a LRM/Garda/Hoshiko fleet operational early is scary.
That said, the assailants do have a lot of indirect perks (typical of the Vasari faction, really). When focus firing capital ships or starbases, fully-upgraded assailants are better than LRM (since mitigation is more powerful in these cases, hence phase missiles provide more benefit). Assailants perform much better against Advent battleballs than the TEC LRM do for the same reason. Then there's the bonus that assailants share their damage upgrade with flaks and fighters. Oh, and assailants also give less experience than LRM's despite costing more.
Personally, I think there's enough room to cast these two units as peers. Yes, the LRM is the stronger one here, but the assailant has a lot of compelling selling points as well. I also should add the Assailants vs Illuminator test isn't exactly valid, since in reality assailants are always mixed with sentinels which will absorb a significant amount of the side-beam punishment.
as they might have lost just because of less health per supply point.
Irrelevant against the LRM, which can and will focus fire high priority targets, so the fragility of the assailant will be exposed by any competent player. This is, however, very relevant against the illuminator where you have no control over the target of side-beams, so a lot of it will be absorbed by sentinels.