It all comes down to personal preference for the most part. There are several types of tweeters available, conventional dome shaped tweeters are built with different materials that will often influence thier sound. Some higher end manufacturers use berylium or other light rigid materials that will extend the frequency repsonse further than others. On the other spectrum you have the soft dome silk tweeters that sound a little milder. However, what is to one man strident, bright, brittle or harsh can be to someone else the perfect shimmer on the high end.
Other tweeters are horn loaded meaning they have a compression driver (typically a piezo driver) loading the throat of a horn. The typical advantage here is that they are very efficient at converting electrical energy to acoustic output. A lower powered amp can drive them to much louder levels than non horns. Some would argue that these have a warmer sound to them.
Yet another type of tweeter is a ribbon driver which is somewhat similar (at least in theory) to an electrostat. The Electrostatic tweeer sandwiches a very thin film between two plates called stators. These plates are magnetized and allows for a much larger surface area. The benefit with this is that the driver doesn't have to move as much and sounds more effortless.
Other tweeters are horn loaded meaning they have a compression driver (typically a piezo driver) loading the throat of a horn. The typical advantage here is that they are very efficient at converting electrical energy to acoustic output. A lower powered amp can drive them to much louder levels than non horns. Some would argue that these have a warmer sound to them.
Yet another type of tweeter is a ribbon driver which is somewhat similar (at least in theory) to an electrostat. The Electrostatic tweeer sandwiches a very thin film between two plates called stators. These plates are magnetized and allows for a much larger surface area. The benefit with this is that the driver doesn't have to move as much and sounds more effortless.