I'm not familiar with your cab, so don't know if that's part of the problem or not.
I own both, and as I've posted a few times, I can get the LMII to sound VERY similar to the TF, but not the other way around.
The LMII sounds wonderful to me virtually flat. Try the head with both filters engaged at around 8 o'clock or no more than 9 o'clock. That setting has provided a punchy tone with plenty of low end extension and nice upper treble extension with no harshness through every cab I've tried that head through.
The LMII will approach the TF 'flat' setting with the VLE at about 10 o'clock, the VPF almost off, the bass dialed back to around 11 o'clock, and the low mid just bumped up a touch. Not exactly of course, but it will give you a feel for the more mid punch, slightly compressed low end and 'bright but no sizzle' tone of the TF. The TF sounds great for what it does, and has wonderful build quality.
I find the LMII and TF about the same regarding clean volume, with the LMII having slight advantage to my ear. Of course, there's a 750 watt TF coming out, but that will the almost three times the cost of the LMII.
IMO.
Edit: Both the LMII and TF volume and tone are greatly improved running at 4ohms versus 8 if you have a large cab like a 410... more open, louder, punchier to my ear.