The Sennheiser 650s don't really need an amp to drive them. They're easy enough to drive even with mobile devices which leads me to conclude that your interest lies beyond just simply amplifying the signal to acceptable levels. At this point the conversation becomes very subjective as headphone amps that do more than just amplify are colouring the sound you're listening to in some way, shape, or form. Whether the colorization is acceptable or not is ultimately up to personal preference and no one's opinion will satisfy your inquiry until you hear it for yourself. All anyone here can do is inform you of the differences in the technology to guide your puchasing decision.
Solid Sate Amps are great for amplifying without colouring the sound. If you just need a boost in amplitude, these are the way to go. Most just do the job of amplification and nothing else. These tend to have a colder sound although with anything, it's not always the case.
Tube amps tend to colour sound more than solid state. It usually makes audio signal sound warmer with a slight increase in the mid and low-mid for amps with vintage style tubes. The cool thing about tube amps is, you can easily switch out the tubes to get a different sound, making them a lot more versatile. You can achieve a very analytic cold sound with these amps and the right tubes (usually Russian tubes are more articulate and cold sounding).
Between those two technologies, the only other things to consider is price point and the inclusion of a DAC. I suggest getting a tube amp and then play around with switching tubes out for different sounds. It's the more expandable than a solid state amp.