Here's one situation where a transistor amp has an advantage over a tube amp.

A tube amp sounds best when you push it into 'the sweet spot' where the tubes compress and distort the sound in a very pleasing way. I have yet to hear a transistor amp that truly duplicates this. The problem is, there is not much you can do to adjust the volume of the sweet spot.

A transistor amp will accurately reproduce the signal, at whatever volume it is set to, as long as it doesn't get pushed into clipping. This allows it to deliver the same sound at any level. So, if you were to record your amp at different volume settings, the recorded sound would be the same.

What you're experiencing is a phenomenon related to the way the human ear works. At different volume levels, the ear's sensitivity to different frequencies changes, making quiet music sound kinda tinny and thin. I think you'll find that if you raise the bass a bit and roll off a bit of the treble, it will help.

Something else to consider: are you 'backing off' your playing in order to accommodate the quieter venue? Pick attack on the strings has a big effect on the punch. Dig into those strings, and let 'em ring!