Why is that ? What's the big advantage of these things?

It's the difference in the output. A Klargester output is pretty close to
pure water whilst a septic tank usually outputs only partially treated
sewage. The Environment Agency often insists on proper treatment, rather
than a septic tank.

Septic tanks aren't as effective as they used to be due to increased
detergent use making the anaerobic bacteria they use less viable. A biodisc
constant aerates the water, allowing much more robust aerobic bacteria to do
the work. A septic tank will usually require more maintenance and pumping
due to the lower reliability.

AFAIK, they have moving parts and require electrickery. Neither of these
are attractive features. Is it worth it?

Yes. However, if you really worry about the electricity/moving parts, they
do another model called the Airflow which has neither, but I suspect isn't
quite as effective, and might be considerably larger, although I'm not sure
about this.

Christian.