These are just my personal observations... may or may not be useful for you specifically.
Continental 'Mountain Kings' - hard compound, long-wearing, thread pattern knobs are well spaced and sheds mud really well. It's excellent and predictable in mushy damp slippery clay, and it stops really well on pavement and dry hard pack soil with or without dusty loose layer on top. This is the cheaper tyre... which is my BEST all-around favourite (for my skill level, riding style, and areas where I ride). It loses traction quickly over loose pebbles during sudden braking, but then again most tyres do. I've been meaning to try their better 'Trail King Protection Apex' with black chilli compound which should excel in the same conditions according to their website.
Maxxis Minion DHF / EXO Protection - this came stock on the front of my new Trance e+Pro, can't remember seeing what compound it was (medium hardness from what I remember). Excellent braking on dry hard pack and on pavement but the rolling resistance was too much for my liking. Draggy, like the brakes were left on. Numerous closely spaced knobs logged up easily with mud. It also had this nasty tendency to pick-up stones and flick them ahead which inevitably hits me on the face... it had to go.
Maxxis High Roller II, 3C Maxx Terra / EXO Protection - rubber compound feels soft and tacky (leaves a mark on my workshop floor. Seems to excel over dry loose pebble/gravel, loamy pine forest beds, and hard pack soil - will still lose traction under sudden braking but not as quickly as the Mountain Kings. Rolling resistance is quite low considering tall knobs and is surprisingly quiet and speedy over pavement. During a sudden stop over pavement (had to avoid a car), it skidded whereas the Contis would not have. Haven't ridden these in mud yet, so I have no idea if the softer compound will translate into better or worse traction in the wet. The early 26" High Rollers I've had in the past, shed mud really well too.