I had Shinx as my Partner in Sky and I'd say he's excellent! He gets the Egg Move Quick Attack to start off with, which is quite helpful.
And yes, Shinx learns Discharge at level 41, which makes him very efficient for those infamous Monster Houses.
He gets Bite, which can make the foe cringe, and Crunch which can lower Sp. Def. by level-up, as well as Spark and Thunder Fang, which are solid Electric-type moves. On top of that, if Discharge isn't enough, Shinx can learn Thunderbolt from a TM to hit every enemy Pokemon adjacent to it (as well as Shockwave, which attacks long distance in straight lines and has perfect accuracy).
Also, Shinx is part of the Group C IQ group... these Pokemon tend to learn skills that are very useful in combat: Intimidator, Nonsleeper, Extra Striker, and Brick Tough, to name a few.
Based on my experience with him, he's a sturdy, reliable Pokemon. And Discharge makes him a real winner.
So personally, I thought Shinx was a great Partner, plus his little facial expressions that are shown as you progress through the story are pretty cute. (=