Each time you shift, the shifter pulls the cable a fixed distance (for Campy, the distance varies slightly, but functionally you can ignore this). That's called the cable pull. Then, for each mm of cable pulled, the rear derailleur moves a set amount, known as the actuation ratio. For example, I believe that 11s Shimano road RDs have an actuation ratio of about 1.4, i.e. for each mm of cable pulled, the RD moves 1.4mm horizontally. I believe Shimano 11s road shifters have a cable pull of about 2.7mm per shift.
These quantities vary slightly for Campagnolo 11s shifters. Arts Cyclery used to have a blog post with the numbers, but it may have been taken down. I believe that the actuation ratio and cable pull are 1.5 and (an average of) 2.6mm respectively.
When people say that Shimano and Campy 11s are compatible, they mean that if you put a 11s Campy wheel in your otherwise Shimano bike, it will shift properly. The reverse is also true. You're generally not recommended to mix each brand's shifters and derailleurs. The numbers for 11s groups seem pretty close, but the errors will add up over the full cassette. That setup is not guaranteed to work.
Also, Campy has a different chain of spare parts. In particular, when you need new shifter hoods, you'll have to find someone who stocks Campy. Campy shifters also take slightly smaller shift cable heads, although I'm not sure if ordinary cables are effectively interchangeable. Anyway, if you aren't going to make the whole bike Campy, then I would question if swapping the shifters alone for Campy is worth it, even if the rear derailleur was compatible.
Last, the brake's cable pull ratio, if you were using cable actuated brakes, is slightly different between Shimano and Campy. For rim brakes, you are probably a bit better off keeping the same brand's brakes and shifters paired. For hydraulic systems, 11s Campy shifters use mineral oil. I believe that when introduced, it was blue Magura oil. The 12s system has switched to a red oil. Magura and Shimano oil have been reported as interchangeable in practice, although Magura and Shimano both have sworn that the oils will destroy the brake seals. If you were talking about using SRAM shifters (which use DOT fluid), this would most definitely not work, and you would wreck the seals for sure.
That said, as a side note, a Campy front shifter will shift a Shimano front derailleur. I know this from my cyclcross days, when bikes frequently had 'Frankenstein' drivetrains.