"Mark Tremonti's Guitar Gear Equipment and Rig" mentions his amp's settings, and amp types. That's a starting point. Note that it says he uses a "Bogner Uberschall for low end", so on your X3 try setting up a dual-patch with a Rectifier head and cabinet, and a second stack using the Bogner amp model. I don't remember which one it was, but I'm pretty sure they have one in the Pod X3.
Even with the exact same amp, cabinets, guitar, cables, effects, picks and maybe even clothes, you still won't sound like a particular player. A lot of their sound comes from their fingers and picking attack and even attitude.
Besides that stuff, a couple things might help. Have you tried:
- Drop-D tuning? The song you link to has that low note that sounds very drop-d-ish.
- Cranking the bass on the amp isn't necessarily going to give you a full bass sound. On a lot of amps it will give you a muddy, or flabby sound because the amp can't handle the power demand. A Pod X3 (which I also have) will model the performance of a particular amp, including its (in)ability to stay clean at particular settings.
- Cabinet types make a big difference. I've gotten better solid lows out of the modeled Rectifier 4x12-type cabinet than I did from the Marshall imitations but you might not like that particular sound.
- What type of guitar and pickups are you using? Hot pickups can push the amp-model too hard so backing down on the volume might be necessary. Unfortunately, the X3 seems to suffer from impedance loading worse than a real tube amp, so your sound might get muddier than you want - it's a balancing act. Also, humbuckers seem to get muddy faster than single-coils, especially when you roll the volume back.
- What are you using to monitor your sound? High quality headphones designed for studio work? Plugging into a stereo system? Running into a power-amp then to some high quality keyboard cabinets? Or, are you plugging into a combo's input jack? You want to remove external influences from the sound. I set up my patches using a good set of Sennheiser over-the-ear headphones plugged into the headphone out of the X3. I get the same sound going into the computer that way. My amplification comes from the power-amp section of a Line6 Flextone III, skipping its pre-amp and modeling. It's a very clean amp so the X3 sound isn't messed up like it would be going into a regular guitar amp.