This is a tough question because there is so much variety in tube amps. They all sound different from each other depending on the tubes used, the type of circuit it has and what the power supply is like.
First, look at the most important part - the power supply. You can change AC into DC with either solid state or tubes. An amp with a rectifier tube sounds different from an amp with diodes to rectify the power. Some tube amps use chokes to further smooth the power. Power supplies with a choke (or several) tend to sound better than ones without. Also, sometimes the amp has regulated power. There's debate whether it helps the sound, but there will be a difference whether you regulate or not. Just like rectification, you can regulate with tubes or solid state and each has its own sound. Finally, look at how the tube filaments get their power. You can use AC or DC for the filaments, each with its own sound. If you run DC, or you can also choose regulation and rectification methods.
Next are the tubes. There is such a wide variety of types and styles that it would be difficult to give an overview. One important difference is between indirectly heated and directly heated tubes. Sometimes the filament carries the signal and sometimes it is separate, like a light bulb. Directly heated tubes have a charm all their own, however, and are sought after by aficionados.
The circuit is also hugely important. Again, there are many varieties and subtle variations. But the main topologies you'll find are push-pull, single-ended and OTL (output transformerless). Each has its own signature and style, often very different from the others.
The output of the amp is important, too. You'll find them to be either transformer coupled (usually single-ended and push-pull amps are) or OTL. There are variations and exceptions, but you'll find sonic variations between the two.
If you're looking for the classic "tube" sound, try a single-ended amp with output transformers. A tube on a transformer is the sound a lot of people think of when they consider the classic tube sound. An OTL, generally speaking, is faster and brighter.
The difference in price between amps is usually a function of the complexity of the power supply and whether it has output transformers. Generally, the more expensive amps have more transformers, chokes and other parts in the power supply. Since the power supply is fundamental, and you're reall listening to the power supply, the better conditioned the power is, the more refined the amp. Also, quality output transformers can run $200-$500 and up for a pair, so those add significantly to the cost.
You'll find the least expensive amps to be OTL, with just a simple power/filament transformer and diodes for rectification. You generally won't find regulation, chokes or other methods to refine the power. The selling point for most of those is tuberolling. Tuberolling has its place, but My take is that you're much better off saving the money on extra tubes and instead putting that towards an amp with a high end power supply.