I would also say go for the ventrac. The videos they have on you tube are pretty impressive. Probably would depend on how hilly I guess not sure of the cost of the ventracs nor do I know someone who owns one. A 4wd would probably get you around pretty good too.
Depends on what you mean by "hilly". Have you been mowing it with the old Deere? If you got by with that, then the first step up is a 4wd mower. Deere and Kubota are probably the top brands with that type of equipment. Both make top notch products. Next you can go to a 4wd "subcompact" tractor. Bigger, more rugged than a lawn mower; does a lot more also. Same brands, plus a few others to choose from. If that's not good enough for your hills, look at some of the more specialized machines. Ventrac and Steiner are two outfits that make mowers for very hilly property.
Be prepared for sticker shock... any time you get into 4wd and equipment with increased capabilities, the price tag goes up. Don't use "lawn mower from Sears" as your budgetary reference; these things are more in the "new car" bracket.
Obviously you need something sized for your 1.1 acres, not some of that big stuff.