Just my $.02 here, but for stuff like this I usually go with generic simply because of the price difference...at least when it comes to Canon. "Genuine Canon Accessories" tend to cost a bundle compared with thier generic counterparts.
One big thing to consider though is, if the camera is still under warrenty, then for something like a battery grip, you may wish to stick with Canon as I've heard rumour tell that using non-Canon batteries can void your warrenty. Canon tends to be a little...err...fussy about using non-Canon equipment to begin with (of course they are...they want you to spend your hard earned money on their gear, not someone elses!). They're a little notorious about not releasing their production notes to 3rd party vendors and such...hence why most flashes don't work well with Canon's ETTL flash system. Regardless of that though, if you're like many people and really concerned about the warrenty, then you may wish to stick with the Canon grip.
Now with that said, again I usually use the generic stuff myself. Since the warrenty is expired on my Rebel XT, I get my batteries off Ebay for example...instead of paying between $60 and $80 a battery, I get them for $2 a piece. Never had a single problem. My remote is also generic from Ebay...it was like $6...works like a charm. Also, until recently all my lenses were either Tamron or Sigma. Now I have encountered one little glitch with the lenses...I have to turn the camera OFF between lens changes otherwise the camera errors out (which really isn't a big deal). I've also had the problem with flashes...I stood there in the camera store and was trying brand new flashes right out of the box (Pro Master brand) that wouldn't work with Canon's ETTL. With most of them, the flash wouldn't even fire. I was fortunate enough to find one that did work in manual mode though so I grabbed it! Sure the Canon 580EX II speedlight would be much more trouble free, but then I only payed $70 versus $500.
To me it's a toss up really. -IF- the price was the same...or at least close, then I'd go with genuine Canon equipment. However that's simply not the truth of the matter. Genuine Canon gear is expensive and usually I don't have the bread for the nice toys so, as they say, one learns to make do with what one can afford. In otherwords, when I go to get my own verticle grip, I'll probably get a generic off Ebay myself...as well as a generic angle finder and pretty much everything else! LOL!!!.
Not sure if that helps or not, but good luck!