There is a fundamental error in that design as shown. It's actually two mono limiters, working independently. If the limiting action isn't the same in both channels, the stereo image will be seriously messed up!
I've built limiters (and compressors) using the 2081 (and 2180) VCA chips, and the results can be exceptionally good. I added the left and right inputs together through a couple of op-amp buffers to feed a common sidechain I built a bargraph indicator to monitor the VCA control voltage, thereby showing the amount of gain reduction being applied. My sidechain used full-wave rectification of the audio (using an "ideal diode" op-amp circuit), and the time constants for attack and decay were "program dependent", making the operation of the limiter less obvious to the ear. Without using delay line methods, the basic limiter is prone to overshoots - it can (effectively) reduce the audio too much, causing a post-peak "gap" as the gain recovers to normal. This can be minimised by sensible choice of time constants, but will always be a compromise with a basic limiter, and you'll always need a post-limiter clipper to prevent over deviation on peaks.
A more sophisticated approach - without "going digital" - is to introduce a delay into the audio path, with the sidechain take-offs before the delay, and the VCAs after the delay. With the right selection of delay (roughly the same as the attack time of your limiter), you can eliminate overshoots and pumping whilst keeping really tight control of level. This is so good that it obviates the need for a clipper after the limiter to prevent sudden peaks getting through!
The classic delay line topology - as used in the 1970s Pye broadcast limiters - used capacitive and inductive "all-pass" networks, cascaded to provide a flat frequency response over the audio range. This was incredibly expensive and required dozens of custom-wound coils. My approach is to use "bucket-brigade" delay ICs, overclocked to give a very wide bandwidth and to move the clock noise (and other artefacts) well into the ultrasonic. I used MN3007 ICs (they have to be genuine Panasonic ones) clocked at about 410kHz for about 1¼ms delay, with the sidechain attack time constant set at the same..... In use, the delay is imperceptible - it's just like the monitor speakers being (roughly) 13" further from the listener! On headphones, you can't notice the delay between your speech and it appearing in your ears!
Practically speaking, the MN3007 S/N ratio is slightly over 80dB, which is not much worse than the rest of the audio chain, all noise sources considered. Its distortion is also not too bad - and much better than the distortion introduced by clipping if it's needed!