I just picked up a Savage Axis from a guy in a hell of a deal last week and really like it in this class of rifle. With that said, last hunting season 3 guys who work for us came to our company ranch and none of them had rifles when they were invited. All 3 went and bought the 770 with scope and SS barrel. 2 in .270 and 1 in 30-o6. I helped each of them site them in, and I must say that while the Axis does feel a bit nicer and better built, the 770 is a nice value and will get the job done just fine. They all were very happy with their purchases. The glass did pop out on one of the guys scopes on the first round though, but he bought the floor model due to it being the last in stock, so no telling what happened to it before he got it. I also like my Savage Axis though and the Stevens 200 is also made by Savage and a really nice gun in this rifle class.
ETA: My opinion is based on the OP saying he would maybe hunt a few times a year. He probably wont put half a box of shells through it a year. To be clear, if I had a choice and could only choose in the economical rifle class, I would choose the Axis for sure.
This post was edited on 7/31 at 2:56 pm