Hi-Jump Kick is probably one of the best moves ever, that is, if it attacks. If it doesn't, then very undesirable consequences will be faced.
Hi Jump Kick has a 10% chance of missing. Think of every ten times you use the move, it will miss only once. As for Drain Punch, you will damage the opposition, and regain half of your inflicted damage from the previous turn.
As much as I want to scream Drain Punch, I'd actually go Hi Jump Kick. I mean, when you miss, yeah, you've guaranteed yourself to faint your Mienfoo. However, in the cases it hits you've guaranteed their team a faint to their Pokemon. It's a very risky situation, but it's a good risk to take, I think.
I know this is probably the most illogical answer on Pokebase, but it's my opinion.
Drain Punch is still something to consider though. You can get back some HP from the opposition's previous attack. This is really helpful when, for example, in the Elite Four they use an incredibly strong attack. Drain Punch! Half of it is regained.
The only time you guarantee yourself a miss with Hi Jump Kick is (there are many more scenarios than this, but I get this one the most, and I utterly fail with it) Double Team. Double Team applies with any move really, so if your opponent uses it I beg you not to use it. There are also moves like Dig, Fly and Dive that are like that, but they rarely occur in the game. And even when you encounter a move like that, Mienshao has 105 Speed. So you'll be bound to attack first.
Well... sorry about this wall of text.
I tend to do this a lot. xD
Good Luck! :)