On the left you can see the inverted dome, which enters through the phase plug with 4 expanding conical tubes, which combine at the throat which is also a conical tube. A horn or waveguide would be attached to the throat. It might be as large as 18" at the mouth. The advantage is clear - a very small lightweight piston can extend to high frequencies and yet it's tiny movements are coupled to a much larger area at the mouth. So you have the best of both worlds - the extension of a small light piston and the power and efficiency of a very large transducer. At the same time, the waveguide allows control of the dispersion. With a dome tweeter, the dispersion is controlled by the small size of the piston.
Here is another example:
Compression drivers can be used for high frequencies, midrange and even bass.
CDs vs domes
A dome tweeter will typically have about 90 db sensitivity and wide dispersion. It's dispersion if fixed by it's piston area and can only be changed by adding a waveguide. In this case a phase plug is needed and it's generally not as effective as using a CD which is designed from the outset for horns or waveguides. The dome will typically handle crossover points down to about 2 kHz with about 100w power handing when inserted into a speaker.
A compression driver intended for high frequencies will have a 1" exit and similar extension just shy of 20 kHz. Sensitivity will be around 108 db and while the power handling may be similar on paper, it applies to a lower crossover point and once padded to match the sensitivity of even an efficient 15" driver, it will have a power handling of at least 1kw and far greater output. The directivity can be controlled and matched to the midrange driver and so it is much better suited to custom design.
THX reference levels
The goal for a THX system to match the commercial cinema is 105 db at the listening position. This is the level reached in a commercial cinema when sitting 2/3 into the auditorium.
Seating distance: 3m
Power amp: 100w
Attempt 1: dome tweeter
First, let's try to achieve this with a dome tweeter. We start with 90 db at 1m with 1w. In theory, 10w yields 100 db and 100w 110 db at this distance. At 3m the level will attenuate between 4.5 - 9 db. So the tweeter level will be between 100 - 105 db. Power compression will rob some of that output by as much as 5db at the full rated power, but we can expect less for short bursts. So in the worst case scenario we get 95 db which is half as loud as our target. In the best case scenario we only just make it to the target and it's likely that the tweeter will struggle. If the amp is clipping, then the tweeter may be at risk and the sound may indeed be quite harsh. The ear becomes more sensitive at this level, so any problems are heightened.
Verdict: 100 db is probably the useful limit. A little more is probably possible, but undesirable.
Attempt 2: compression driver
Now let's try it with the tweeter that is meant for this kind of output. The right tool is the one that can do the job with a decent amount of headroom. We'll start with 108 db @ 1m with 1w and 118 db with 10w. If we double that power twice, we get 40w input and 124 db. The amp will not clip at this point so we are in a safer region. We'll take the conservative distance compensation so we get 115 db @ 3m. We now have twice as much output as our target, so in reality we can dial the power back so that we reach our target with only 4w!
Applying the same rules as we did with the dome tweeter, we can get 118 - 123 db output at the listening position, but this is far more than we need. This level exceeds many rock concerts.
The point should now be clear - compression drivers are the right choice for reaching THX reference levels. However, if used well they have other advantages as well, including most notably the ability to control directivity.