Mr. Hetfield, I'm not sure but I think I know exactly what you're saying. But, it does get better!
I played Line 6 amps for years. Started with the AX2 and eventually moved up to the Vetta II (after also trying some POD stuff). Anyway, when I first started trying out (and eventually buying) some tube amps I noticed the same thing and I think it has a lot to do with the "feel" of the amp set up.
I almost always played in 3 piece bands as the only guitar player. With the Line 6 stuff I was able to do things with different affects (built-in) what would alow me to really fill out the sound (especially in stereo) and hold things up. However, that being said, they were always missing that "tube tone".
When I first bought a Stilletto I loved the tone (or thought I did at first) but I had to adjust my playing style because it was a lot less forgiving. When I would a/b it to my trusty AX2 I always thought the ax2 sounded better and more full. And it did because I was using chorus and delays and other affects that made it sound bigger.
The solid state stuff (atleast what I had set up) was easier to play becuase it seemed to "smear" the tone (for lack of a better term). It wasn't very articulate like a tube amp is. It's almost like what you hear out of the modeling amp is what you would hear after a guiatar part was over processed as part of the final mix/mastering. In other words what you think a guitar sounds like when you listen to a CD. Also setting up the eq on a mesa takes a little getting used to until you figure out how to get what you want out of it. But it will always be different (in a good way) compared to a modeling amp. You will hear things that the modeling amps can't reproduce (i.e. tube tone)
Another thing I came to realize about modelers vs tube amps. A line 6 modeller can sound awesome by itself! You might think that because it sounds so good in your bedroom or garage that it sounds as good in a band situation. I can tell you from experience that this is not always the case. In contrast, a tube amp may not sound like what you're expecting to hear by itself (or at least not what your brain thinks it wants to hear) but together with the band sound awesome! You really have to take the time to listen to what you're hearing on CD's. Most guitarists dont use as much gain as you might think. And probably if you listened to the raw guitar track by itself (even of you favorite band) you would probably be surprised what it sounds like before its mixed, colored and processed.
So anyway, to stop rambling there are a few things I can tell you from my experience with SS amps.
You will have to adjust your playing style a little and you will really need to tweak the tube amp until you find the voice you're looking for. Trust me there are settings in there that will affect how it feels when you play it.
Dont think that if it doen't sound good by itself that it will sound bad in the band. As a matter of fact I had to re-learn how I listened for the tone I was going for knowing that it would sound different in a band situation.
The preset tones on modelers tend to be overly compressed. Which means you can really bang on the guitar and it will still sound good. On a tube amp playing style and dynamics really come into play. There is some natural compression going on in a tube amp but it's not the same thing.
I have a Roadster now and I love it. I use an overdrive for a clean boost sometimes and use a chorus pedal occasionally for cleans. I am still adjusting my playing a little to get used to this amp but it's all for the better. It makes you play better in the end.
Hope this helps.