The guitar itself isn't going to make much of a difference in terms of the heavy, high-gain tones, but the pickups certainly will. Beyond that, the basis for your tone is how good your amp and speakers are.
So... its hard to say, but if you're happy with the basic tone of your amp, then try out some different distortion pedals.... Line 6's tone is based around digital algorithms, while your normal distortion pedals are based around analog circuits... this analog component is to some degree the "true life" sound you're talking about.
As a rule, I do not like Line 6, for a long list of reasons that would be a huge distraction if I started listing them. I will however say that some of the Line 6 clean tones are pretty decent. So, one of the options that I would explore would be adding a distortion pedal of some kind to get closer to a different tone that you might be interested in.
If you aren't happy with the basic tone of your amp, then you're looking at getting a whole new one... not necessarily a cheap proposition. The only other one that I'm aware of (since Line 6 amps don't have a $#&(@ effects loop) would be replacing the speaker. Unfortunately, I'm not aware of a suitable replacement, ie one that would work well with the higher frequency demands of a modeling amp.
My two favorite distortion pedals are the Boss Metal Zone (for 80's style metal and lead guitar) and Boss Metalcore (for 00's metal and rhythm guitar).... I've used them quite a bit when I haven't had an actual amp distortion to fall back on.
Normally one of the most powerful things you can do is put some EQ (ie like an MXR 10-band pedal or a stereo rackmount 13-band EQ) after your distortion. Of course, since Line 6 doesn't have an effects loop that option doesn't exist.... but you can put EQ after a distortion pedal, and have that signal go into a clean(er) channel in the amp.
Saul