What, tubes make heat? Who knew? The thing is, in a phono stage you’re barely going to notice it. They aren’t going to tax your A/C or keep you warm in the winter.
This is kind of like asking which type of DAC is better - R2R, delta-sigma, or FPGA.
The answer is the same. It depends. On everything else. The implementation of the specific type of technology, the rest of your system, your listening preferences, etc.
I don’t have any experience with either of the two phono stages mentioned, so won’t make a recommendation, but I have heard much more discussion about the Hagerman Trumpet and it has been overwhelmingly positive.
I have a tube phono stage with my main turntable, a solid-state unit with my secondary table, and tubes with my other three turntables. I’ve yet to experience any heat issues or have a tube go nuclear in one. I wish I could say I’ve been so lucky with tubes in amplifiers, but tubes in phono stages and preamps are under a lot less stress than the the power tubes are in an amplifier. My better tube phono stages are extremely quiet, more so than the solid state unit.