The first thing that strikes me about your question is the fact that the Ultegra disc brake is hydraulic as there is no road mechanical disc brake caliper at the Ultegra level. As such, one cannot mix brands of hydraulic brake levers and hydraulic calipers. Although both Shimano and Campy use mineral oil, the specs of the hose and it's fittings differ between these brands. More critically, the amount and rate of fluid transfer from the master cylinders (within the levers) varies such that the opposing brand's caliper response is goofed up. So, a Campy brake lever would be incompatible for an Ultegra disc brake caliper.
In the first part of your question, I've decided that your use of the word, "mechanical," refers only to the shifting aspect and not the braking, which if we're looking at the same systems in both parts of your question, remains hydraulic. As an aside, Shimano and Campagnolo's electronic shift systems are incompatible between one's shifter and the other's derailleurs due to wiring and battery differences. I doubt the software would play well together sans hacking ability of the user.
Strictly speaking, there is incompatibility if one wants to mix Campy & Shimano shifters with the other's derailleurs. This is due to differing cable pull ratios between brands of shifters. Also complicating things is Campy's use of variable spacing between cassette sprockets. At the 11 speed level the differences at the cassette are minor enough that one can use a Campy cassette with a Shimano shifter/derailleur with only a small reduction in shift quality. Mixing the brands' shifter and derailleur however would create a situation where the rear derailleur would move incorrect distances in relation to the sprocket spacing and cause noise, ghost shifting, no shifting or over shifting. Apparently a company called J-tek makes a product called shiftmate which corrects the mixed brands' shifting incompatibility by altering the amount of cable pull that reaches the derailleur. However, the bad news comes at the end of that long list of combinations possible with a J-tek Shiftmate I've linked to above when they note in their comments under Shiftmate X, subheading, Campagnolo 11 speed shifter with Shimano 11 speed road or mountain derailleur: "CAN'T BE DONE."
Anyway, in researching this answer, I came across this Article on mixing road bike components. It's a pretty clear summary of what's known about the effects of mixing components from different groupsets, not only from competing brands, but also various models within the same brand.