Both have a lot of attractions but I would choose Denver though the skiing would be farther west like to Vale, Salt Lake has no skiing either that would be in Ogden, but if skiing and hiking is what you are looking for you need to go farther north, to Montana, Big Sky has lots of skiing and hiking is all over, plus you have good skiing at Bridger Bowl, and Yellowstone has cross country, snowmobiling and hundreds of miles of hiking trails.
I especially love Rocky Mt. National Park, but the scenery is beautiful in both places so you can;t go wrong with whatever you choose. A lot of the tourist attractions in Salt Lake City have to do with the Church.