I would choose the G2 if you plan on using it for Rimfires, .223's, and light deer calibers...if you want magnums, or think you need bigger calibers at some point, go with the Encore, as long as you dont mind the extra weight.
Calibers like the 7x30 Waters in a G2 are fine for deer out to 250 or so, and thats about as far as i ever shoot anyway, no matter what caliber i am carrying, since i usually hunt areas where i cant see over 100 yards...if you do plan on using that gun to go chase elk or something big, guess the Encore would make more sense...