One of the best specs for determining whether an amp will work for headphones is the output impedance. Unfortunately, most won't tell you what it is. I see several manufacturers claiming that their OTLs "work" with low impedance headphones. This is generally not the case. If the output impedance is higher than the headphone impedance, things get hinky. It usually shows up with bloated and lousy bass. Some people seem to enjoy the bass bloom, but I think it sounds awful.
Some manufacturers play games with output impedance using negative feedback. That's feeding part of the output signal back into an earlier stage. It does make the output more linear, but too much NFB strangles the sound. Nothing is instantaneous, so the time it takes for the NFB to go back fiddles with the timing. NFB also lowers output impedance, so sometimes it gets turned up much too high in order to make the amp work with lower impedance headphones better, but it also mucks up the sound. Of course the salesman won't tell you that.
Solid state doesn't have any problems with output impedance, it's naturally low. Tubes only have a low output impedance if you put them on output transformers (expensive) or use something like a 6C33C which has a low output impedance.
Power supplies are very important. Solid state, generally, is cheap to power. It usually runs around 12V-24V so you don't need the heavy-duty expensive iron for the high voltage tubes need. Tubes often run at 200V or more, so the bigger iron costs more. With solid state, you can use inexpensive chips and capacitors to turn the low voltage into clean DC. For high voltage, tubes need big caps and, preferably, chokes to really get clean DC. You've probably already figured that those cost a lot more. Clean DC is hugely important because that's what you're listening to. If a power supply lets some AC noise through, that AC noise ends up in your headphones. Cheap tube amps skimp on power supply parts - that's the easiest way to lower costs. If you want to do a tube amp the right way, you can easily spend $500 or more just on parts for the power supply.
In short, it's easier to do solid state the right way on a budget. Solid state might not be as sexy as tubes, but it will deliver excellent sound on a budget. If you want tubes, you either have to buy one of the better ones or build your own.
Construction is also important with tubes. Cheap ones put everything on a PCB. I don't like that because PCBs are generally meant for low power applications, like solid state. Too much heat can damage them and once a PCB is damaged, they are a pain to fix. Lifted or broken traces require jumpers or heavy surgery if they can be fixed at all. Also, I'm not keen on running high voltages on traces. I'd rather put them through high temperature rated wires. This is why I think tube amps should be built point-to-point. Point-to-point costs more, but it can always be repaired. Also, it keeps the circuit paths a lot shorter since you can built the circuit in 3D instead of 2D. There's more labor involved in point-to-point, but you get a higher quality amp.
