If you run, you will get a stronger forefoot, your hip flexors are called into play much more, your quads and hamstrings both have a very active role, as well as your calve muscles. You must swing your arms and bring your core into the motion. There is a huge emphasis on landing and pushing off, your shoes are important, as well as the gait of your foot, your stance, and whether your an overpronator or underpronator.
I would say running is more taxing on your knees and joints.
If you want to bike, your bike will be more important than shoes, however shoes will still serve their purpose (try laceless ones if you get serious). Your quads and hammies are both activated, as well as your calves, but not to the extent of that in running.
Your core is much less activated, your arms are not activated unless you're turning, even then it's minimal. You get places faster, you can cover much more ground while on a bike. It is less taxing on your knees. More cushioning for your whole body, but I would say in general less of a full body workout than running.
I can appreciate your love for the outdoors, and personally I found running kept that love at the forefront of my run, where as when on a bike I am more focused on not running over large objects, dodging children, and when I can I will take a minute to enjoy my surroundings.
I am not a scientist, I can't justify my reasoning, I just know what feels right, for me.
Best of luck friend.