The first time I heard and felt a difference between a tube amp and a solid state amp was a very specific thing. Maybe you can recreate it next time you play though a tube amp.
I played on a Fender Princeton Chorus red-knob for 10 years (A solid-state 25 watt x 2 channel stereo 2x10). So every little thing about how my guitar sounded through that amp was very familiar to me. Then one day I played through a friend's Peavey Classic 50 4x10 in his jam room. So we had total freedom for volume. A 50-watt tube amp through 4 10" speakers is nothing to sneeze at, its pretty loud. I turned the post amp gain to 7 or 8, put the preamp gain to 3 or 4, and played a song of mine that I'd been playing for years. Blues/rock Stones/Allman Brothers kinda thing.
I played his Fender Coronado semi-hollow through the amp, not my normal guitar either. I play a LP Classic so a semi-hollow Fender is pretty different. But still I could hear the difference every time I played any notes in first position on the guitar. Anything within the first 5 frets had a sweetness that I'd never felt or heard before. Mainly on the bridge pickup but I could detect it on the neck pickup as well. But every time I let a note on that area of the neck ring out, or bend it up, it was just so appealing.
Shortly thereafter, I started shopping for a tube amp of my own. Due to available features and a match for my tastes, I settled on the Traynor YCV80. A quick aside: a 50-watt 4x10 is pretty damn loud. But an 80-watt 2x12 is even more painful when cranked. Watch your wattage and don't buy anything that you can't crank regularly. If you can crank a 100 watter without suffering hearing loss or a disturbing the peace citation, more power to ya (hey a pun!). After fiddling with the combination lock of a gain structure, I settled on similar settings to my friend's Classic 50: low preamp gain and high post amp gain. Suppliment with pedal overdrive when necessary. Hit it with a compressor/sustainer with a lot of makeup gain and a low threshold to hold it in the sweet spot for solos and big riffs.
The other big difference I hear is upwards of the 12th fret on the lower strings, especially on the low E string. The more post amp gain, the more I hear this difference.
I also love the sound of open strings ringing out with similar settings as I described above but with my TubeScreamer set to totally neutral settings (all 12:00). Oh man an open A string ringing out with these settings? Fuggeddabouddit!
Try some of these specific things on a tube amp next time you get a chance to crank one up. If none of these things make a difference in what you play, then maybe a tube amp won't be worth the investment. Or maybe once you plug into one you'll find specific things that sound more or less pleasant to you.