To answer your question, the G17 is the original with a barrel length of 4.49 inches as compared to the G34 which is marketed as the "competition" model with a barrel length of 5.32 inches and a longer sight radius...so for target shooting on the range the nod would go to the G34, IMO. Both have a standard mag capacity of 17 rounds, with non-standard mags holding more.
I love my 34. The only thing I will eventually change is the sights on it, not fond of the the adjustables from the factory. Aside from that, the 34 is a solid performer right out of the box.
I used it as my CCW for a week while I was having a minor repair done on my 5" 1911. Although it's not ideal for it, I was actually able to conceal it very comfortably. I guess being a bigger guy makes it a little easier to conceal a bigger gun.