The MK23 was designed to fill a USN NSW requirement that included mounting dawn-age target acquisition devices (laser/white light aiming modules, suppressor, etc.), while delivering exceptional combat accuracy using .45 ACP (and with higher magazine capacity). A pistol that could come out of the water shooting as some SEAL was scaling a GOPLAT in the North Sea or Persian Gulf.
In other words, a quiet, reliable, long sight radiused sentry removal tool and CQB pistol. Suppressed pistols were still considered an "In Thing" for CQB back when the requirement was let for a Special Operations Offensive Pistol.
The MK 23 delivered on all counts, but at the cost of being a physically huge pistol. Over the years, mountable pistol accessories have all become smaller...and descendant pistols like the HK .45 USP Tactical provide similar performance in a lot smaller package.
The MK23 will out-group any standard military issue M1911A1 (it was designed to), but arguing absolute accuracy in comparison to custom 1911s is a wash, as few shooters can actually meet the accuracy potential of either the HK or a high end 1911. I rarely saw a MK23 drawn from my unit's arms room for other than familiarization fire on the range. The suppressor was the main draw...but with stellar accuracy universally noted. However, nobody ever actually carried the damn things on a hip holster. Simply too big for practical carry except as a tool packed away in a rucksack pouch.
For reliability under adverse conditions? The MK23 was specifically designed for hard use under tough field conditions. If you need to low crawl through muddy fields or infiltrate the surf zone on some rocky beach along the Russian coast...go with the HK. For practical purposes, any well designed high end 1911 is going to deliver about the same reliability...although you might scratch up the semi-custom logo and finish.
Keep in mind, the size of the MK23 pretty much precludes any reasonable hope for CCW carry by normally sized people. I've only seen one or two ever carried in the field (thigh rigs) in the real world. It's not as heavy as it appears, but it is still a huge hunk of plastic and steel.
Two entirely different pistol concepts (both excellent), and you would be wise to go with the one that feels best in your hand.