Tube Amplifier Sound Characteristics

Like any topic, it all depends on how much you want to dumb it down on the spectrum from peer-reviewed white papers at one end and Twitter posts on the other.
With so many variables at play I don't think a simple warm-cool linear scale is enough to make an informed decision. It might let you cross a few brands off a big starting list. 
A more useful but still digestible format might be similar to how some reviewers rate ~10 attributes and score each on a 1-10 scale. Even rating a few amps you know would take some work.

Honestly, I think familiarity with the nature of various tube types is one of the most critical aspects of what OP is trying to solve for, maybe more than the brand name. Joe's tube lore is a good source for small signal tubes, but I don't of anything similar for common amp tubes. 6550s, EL34s, OTLs w/6AS7s, KT88, KT120, KT150 and little EL84s all have their own characteristics that are a big piece of the puzzle. Sure, circuit design, other parts quality, etc. also contribute. 

Choosing tube amps without knowing tube types is like reading the Torah(they don't print the vowels!). It can be done, but is a lot easier if you understand. Cheers,

Spencer

On the left is warm romantic, on the right cool neutral?

Okay having studied your requirements the solution is obvious. Take a clean piece of paper. Draw a rectangle about 5" wide by 2" high. Label the left, "warm romantic". Label the right, "cool neutral". Take a crayon, color this blob yellow. This is your tube amp diagram.  

Now we do the same for solid state amps. Let's use blue for solid state. 

Now if you followed the instructions well you should be looking at a green rectangle. Smack in the middle draw a great big letter "S". Now divide the "S" by drawing a big ol' vertical line right through the middle.  

This is where you will find your amp. The more of these $ you make the better the amp you will find. 

OK I should have stated that I am new to tube power amps. That explains a lot of my ignorance on the subject and I apologize. I know what I hear people saying and about the sonic characteristics of different tube amps and was trying to identify those on the warmer side. So if it has to do with the tubes I know EL34 in triode is warm/romantic. I will read up on KT120, KT88 and 6550

+1 @sbank

I love the idea of a chart locating the sound characteristics of different equipment! One could start by locating house sound on different dimensions. Tonal balance, detail, warmth… great idea.

The ARC Ref75SE is a very high end and much loved amplifier. It does not sound like solid state… on the other hand, the moment you hear it it does not broadcast “I am a tube amp”. It has the house sound of Audio Research. It is a high end audiophile amp that is musical and accurate. It is highly detailed with great and strong mid-range bloom and articulate bass. I know of a number of people upgrading from that amp, but can’t bring themselves to let it go. Unless you are looking for syrupy bass and rolled off top end then this is a fantastic amp which you could easily keep for a lifetime.
Click on my user ID to see my systems… note there is some Audio Research gear in it.

Also remember the sound you get out of your system is the sum of all components.