I have a dual tonearm, dual cartridge setup for stereo/mono playback. Stereo cartridge is a Lyra Atlas Lambda SL and the mono is a Lyra Atlas Lambda Mono, so essentially stereo and mono versions of the exact same cartridge. Both are mounted on identical tonearms (Clearaudio 12" Universal), and I use a dual phono input Boulder 1108 phono-stage.
This allows me to make a rather equivalent comparison. Playing a mono record using the stereo cartridge and phono-stage mono button engaged sounds great. However, it’s nothing like playing using the dedicated mono cartridge. The latter has a lower noise floor, is more dynamic, more detail, and has vastly improved realism and dimensionality.
[this based on info from the Altas Mono manual]
On mono records, the vertical axis of the groove contains no musical information, but it will frequently have noise, in the form of groove damage and dirt. A true mono cartridge is completely insensitive to the axis, which greatly improves the signal/noise ratio. This is one of the largest benefits to using a mono cartridge and why it sounds so much better than using a stereo cartridge with the mono button engaged on the preamp/phono-stage.