I totally agree with PB, who was posting at the same time. I'll go ahead with my post anyhow, as a different perspective on the same issues:
I am hesitant to recommend anything, because "warmth" does not translate easily to measurable effects or design details. We can all hear it, but it's not clear we are hearing the same thing even if we are using the same words to describe it.
The most nearly measurable effect is distortion, specifically second order distortion. To many people, the right amount of second harmonic distortion sounds warm. (Too much just sounds muddy.) Second harmonic distortion in SET amps increases with signal level, reaching a maximum at full power. So an amp with more headroom will sound less distorted, all other things being equal. And the SEX amp has a bit more distortion at full power than the Stereomour, because the 6DN7 is not as linear as a 2A3.
Amp output impedance (damping) also plays a role. The SEX amp has slightly greater output impedance (a lower damping factor) than Stereomour, so its effect on speaker bass tuning is stronger. This will often exacerbate some bass resonances, lending a completely different form of "warmth". But this is highly variable depending on the speaker.
The more gain stages you have, the greater the high-order distortions become. That's why in theory a passive preamp is better. But many people seem to hear improvements with a good preamp, so there must be other things going on that I for one do not understand (yet). So - again - use your ears; there is no better answer than "try it and see".