Things to look out for are IMHO:
1) Comfort
Surely u do not want to sit on something is not comfortable, u probably cannot concentrate well. Some have round cushions, some have those which resemble a bicycle seat. Some are made of leather (synthetic or genuine?), some have velvet. Some have really thin cushions (lower end) and usually the higher end ones have thicker cushions.
2) Stability
If u do double bass, u will surely love ur throne to be stable. Even if u are not, who want to sit on something which feel as if it will topple anytime? Go for double-braced thrones.
3) Backrest
Having a proper posture when drumming is important. Some higher end models includes a backrest for the drummer to lean on or at least support the back while drumming. One should not be slouching when drumming.
My instructor did mention to me about the type of mechanics used for adjusting the height of the throne, IIRC, those which need u to 'turn' the thrones to adjust the heights are better. Some use bolts to fix the height of the throne such as mine (Yamaha)