I have both and I agree with your observations.
The Tumescent is definitely a little darker (warmer) in tone, and also has a little more midrange to my ears. I think you could say it has a more rounded sound.
In our band's set we play about 80% of our songs in standard and the rest in Eb. At gigs I use the Tumescent for standard and the alder LIII for the Eb songs. There is a difference in tone when I switch, but it's quite subtle, not like if I switched from a Les Paul to a Strat. Of course it depends on what kind of music you play - our band plays rock, so picking out the tonal differences in the mix would require a far more discerning ear than mine - to me they both sound great.
I have a basswood/maple top Suhr modern and have had a number of Axis in the past. For me both LIII's have a better tone - if I use the Suhr I have to dial the tone on the guitar way back to about 4 to get it in the same ballpark as the LIII otherwise it's too shrill for me.
When I'm playing though I don't reach for one over the other for its tonal qualities, it's more whichever I fancy playing. Took the alder one to rehearsal this week and used it for everything, next week it might be the Tumescent.
Hope that helps. You can't go wrong with either