the brakes you've got will be fine. If you were to change to disc brakes you would need... new hubs, possible even new wheels, maybe a new fork if the one you have doesn't have disc caliper mounts, possibly even a new frame as there may be no caliper mount on the frame either!
I used brakes similar to yours 18 years ago for mtb racing, they were made by Magura and were fantastic, I never had any issues with them.
I have found hydraulic brakes to be as reliable as, if not more reliable than any cable brakes when they are set up properly.
Probably more than 90% of mountain bikes are sold with disc brakes these days and there are lots of good reasons for this, the same would be said for cyclocross bikes if they weren't banned in UCI races.
I rode the Great Divide last summer and didn't have a single mechanical issue