I'm probably not going to be able to give a very helpful answer. I think you're right that it is hard to generalize the sound of an OTL vs. a transformer coupled amplifier. Within each of those categories lie many different possible amplifier designs. I've heard OTLs that sound thick, warm, gooey with high distortion, but I've also heard OTLs that have exceptional clarity and tend more toward neutral. The same can be said for the transformer coupled designs. There are numerous variables that affect the end result it terms of subjective sound. Typically designs with lower second harmonic distortion are going to give less of what people associate with "tube sound", but other designs choices - e.g. tube biasing, tube loading, fixed vs. cathode biasing, signal path componentry - are also going to affect the overall clarity and tone and the amplifier may sound less "tubey". Signal path capacitors, for instance, significantly color the sound. Active loading vs. resistive loading also makes huge differences in terms of clarity, soundstage, etc.
So it really can't be distilled down to just how the output stage is coupled in my opinion. When it comes to the output stage coupling, generally you should be getting pretty similar damping ratios on an OTL and the high Z tap of a transformer coupled amplifier. Obviously, transformer coupled designs with multiple output taps offer more flexibility in terms of headphone impedance. Now some might say transformer coupling is superior to capacitor coupling (which is typical for an OTL unless you are using some exotic DC coupled output stage), but keep in mind most commercial transformer coupled amplifiers are using cathode bias (aka autobias), which necessitates placing a cathode bypass capacitor, so its no free lunch, you still have a signal cap in the output stage.
At the end of the day, it comes down to the quality of the individual design. A high quality OTL can sound much better than a run-of-the-mill SET amplifier. However, my personal opinion is the ceiling for transformer coupled amplifiers is higher, but you have to get into some uncommon circuit designs to get there, which are only available through boutique amplifier builders or DIY.
I guess what it comes down to is this: if you can't demo the amplifier, buy based on the headphones in your stable and on the amplifier's reputation. If you own headphones of varying impedance, go for a transformer coupled design. If you mainly listen to high impedance dynamics and there is an OTL of high repute you are interested in, that could be a good option too.
Also, you can't really drop a tube from a transformer coupled amp into an OTL with an adapter and make an apples-to-apples comparison. The tubes are used differently in the two circuits, and using a tube with an adapter in an OTL with that it wasn't designed for likely means it is going to have a less than ideal bias point and possibly a very high output impedance, depending on the tube. OTLs use high transconductance tubes, like a 5998, to achieve a low output impedance. Not all power tubes used in transformer coupled designs have high transconductance, so they don't lend themselves well to OTL circuits.