Only spent an afternoon comparing Lau and Taurus, I don't think it's really revelant (I will try to convice my friend to let me spend a week with his Taurus).
I used LCD3 (without fazor), T1, TH900 and Alpha Dog.
We have two different way to present music : Taurus is more laidback and Lau more frontal with more precise layer and separation (dimension of the soundstage are really close). Both have a airy soundstage and the Lau add more density and weight to the sound (I definitly more acoustic pressure).
Two differents signature : Taurus sound's like a SS amp with a little extra of warm, really balance tone. I just find the uppermids section a bit unatural with some timbres. Lau is sounding like neutral tube amp (definitly close to Eddie Current product like S7 or BA sound sig), really natural, organic and musical with all the strengh of SS amp (speed, tension, detail).
Dynamics & speed : The Lau have a bit more micro dynamics, speed & kick.
For me, the Taurus is the natural upgrade for a guy who liked Schiit Mjolnir (same type of soundsig and way to present music).
Alpha dog match better with Taurus, The Lau is too dynamic and frontal for this cans (it's tiring after 30 min of listening).
LCD3 ad T1 sound's better on the Lau. I think the Lau can be the target for people who only own planar headphones (I really enjoy He-6, LCD-2 and he-560 on this amp).
I didn't find TH900 impressive on the Taurus, close to be a bit agressive, on the same price tag, EC Super 7 is more capable despite it lack of tension in the bass section (in comparison of the Taurus). With the Lau, I have a tiny background noise and I'm really sensitive... The best match I found for the TH900 was an EC Balancing Act.
I'm currently waiting for an EC 4-45 for driving my TH900 and LCD3, I will see if it's a better solution for my two favorite cans