In my opinion there are three factors that go into a stabilizer
1. Rigidity. The stabilizer won't do you any good if it is wiggling around when you are trying to hold steady. There are different levels of rigidity and it somewhat depends on how long of a bar you want and how much weight you put on the end.
2. Weight. The weight of the bar (think of it in GPI like an arrow) contributes to the total mass weight of your bow. The lighter the bar is, the more weight you can put in other place, where it will have a better affect on balance, before you reach your total allowable mass weight.
3. Diameter. Smaller diameter bars have less surface area to be affected by wind.
Personally, I don't look for any after the shot dampening from my target bars. I want smaller diameter, lighter weight, RIGID bars that help to balance and steady the bow.
Different materials, different grade and construction patterns of carbon, etc. all affect those 3 points and also affect the price.
The other factor I look at when purchasing is the availability and price of extra weight. I want adjustable weights to get the balance just the way I like it.
AND, like anything else, at some point you pay for the name too.
I have had bars that I thought "felt" like they worked better than others. That may be a product of the bar quality, the way I had weight distributed ... just in my head, who knows. I don't have a scientific way of testing it. At some point though, confidence in your equipment has an affect.
Mitch