Sorry, another question. Are these parts interchangeable as in direct replacements? In other words will the Shimano calipers bolt in where the Promax was with no issues?
Not sure about that specific bike, but there are two types of caliper mounts: Flat and Post (formerly Hayes).
You can get adaptors to go from one to the other, in either direction, Post-->flat or Flat--->post.
cable systems are *mostly* interchangeable in the lower-mid range systems, but when you get into the higher-end stuff, Shimano and SRAM add in things like Servo-Wave™ and such that make them not work quite as well with you mix and match.
TRP and Avid are both very good at solving this issue, as they both have systems that work well with other brand's calipers.
So, hydraulics vs cable? That's the $24,000 question.
Hydraulics are much better stoppers, in nearly every situation. The downside is that you are adding complexity to a machines that is already quite complex. they are typically sealed systems, requiring no daily maintenance, etc, but when something goes wrong, it can be Bad-Day Wrong.
Cable-actuated systems are much more simple and can be repaired (usually) trailside, where a hydro system might not. They're also usually much less expensive and you can typically keep your existing brake levers.
And then there is the TRP HY/RD cable-operated hydraulic caliper. It's a bit of both. it's a hydro caliper, so you get the incredible stopping power of a hydro, but with the simplicity and compatibility of a cable-actuated system. I've got them on one of my gravel bikes and they're quite good, but not as good as a full-hydraulic system.
All perfectly clear, right? ;-)