I couldn't stand it, so I just did a quick/sleazy test...
I have a female XLR to 1/4" cable I use for this and that, so I plugged the 1/4" end into the power amp input of my Thunderfunk 550B (nice quick and very good sounding power amp). I then swapped the XLR end back and forth between my Eden 405 and the LMII with my Skjold Pro Deluxe 5 plugged into each one, all eq/enhance and whatnot "off" on both the 405/LMII "preamps" and the bass preamp.
The Eden definitely sounded better to my ears, but I LOVE that head for recording/preamp operation. That Eden goldenear stuff is really my thing, and I love the way it records.
HOWEVER, the DI on the LMII was FAR from "thin" sounding. It didn't have quite the depth of the Eden, but it sounded perfectly fine, and had good low end... EASILY "PA-worthy"... NO doubt. It'd record ok, as well. Maybe not the best out there, but it's certainly not unusable by any stretch. The Eden did have more gain, which I also expected, but again, VERY usable.
After this little test, I'm starting to really like the "some may be defective" theory.