I've had an interesting time tube rolling with my Conrad Johnson Premier 12 tube monoblocks.
Same ones I drove the Thiel 3.7 and now my 2.7s.
When I had both the 3.7 and 2.7 in the house I was trying to decide which one to keep. One of the distinguishing factors is the 3.7s sounded like they were: a bigger speaker. Even though by specs only slightly extended further than the 2.7, there was a sense with the 3.7s of the proportion of the sound being a big different. Bass went a bit deeper, the scale was a bit larger on everything. The 2.7s seemed like putting a bit of a girdle on - like the bass frequencies were lifted slightly upwards, putting more emphasis on the punchiness of the mid-bass.
I finally tried replacing the 6550 power tube on my amps with the larger more powerful KT120 tubes. What a difference! Bass feels deeper, the scale of everything - soundstage, image sizes - expanded. Now the 2.7s truly remind me of the 3.7s in that sense. Pretty amazing.