Both seem to be uniquely different fighting Pokemon, and could be beneficial in different case:
Hitmonlee
Pros:
- good attack
- good speed
- good movepool
Cons:
- lower base stat total
- not much defenses
Conkeldurr
Pros:
- higher attack
- great abilities
- higher base stat total
Cons:
- small movepool
- very slow
Based on these pros and cons, their main difference is basically speed. They both have good attack, although Conkeldurr has much more. Their defenses are quite similar because Hitmonlee has high Sp. Def and low defense, whereas Conkeldurr is the opposite (good defence; not so good Sp. Def.). Their Sp. Atk is not much of a problem since they're physical-fighting Pokemon.
The only difference that is major is their speed. Hitmonlee would be a good choice if you want to finish of Pokemon quickly. Conkeldurr is more of a laid back Pokemon, but can resist moves due to its high defence and HP. Afterwards, Conkeldurr can attack with it's high attack.
Also, Hitmonlee can learn much more different moves leveling up, whereas Conkeldurr is limited to Normal, Fighting, and Rock - although he has great STAB moves.
Overall, I would go with Conkeldurr > Hitmonlee because he seems like a Pokemon who can stay in battle longer, and take out Pokemon due to it's high attack. Hitmonlee can get defeated pretty easily due to its low defence. But it all depends on your battle style: A Wall or Fast Attacker.
Your Choice! Hope I helped! :)