I had exactly the same problem. I’ve got an American Strat and a Tele (with a bridge humbucker) and just could not get the dirty sound that you are supposed to get on the Line 6 amps.

See my thread here: http://uk.line6.com/support/thread/148053

Now that my DT25 has been fixed, I can even get a dirty sound on the clean amp settings by just turning up the Drive knob.  

Master volume on the DT25 needs to be up at least around 12 o'clock to get the natural OD you'd expect from models like the plexi and park. Below about 11 or 10 o'clock I could never get the DT25 sounding like a rocking amp in normal mode. In LVM, there's modelling going on in the power amp section.

A lot to do with how the power amp actually works in normal or low volume mode. Doesn't affect the high gain models as much, but for classic rock tones with switch2, they mimic the amps they are designed on in that they are cleanish sounding at low volume or when guitar's volume pot rolled back. I've tested this a lot at gigs and at home and I'm sure its no amp fault, as much as design.