The efforts are not distributed the same way. Obviously biking will exercise your thighs but not much else. While running uses abs, all your legs muscles groups. I also believe that we're wired to be efficient at running and thus running tickles your body in better ways. Also there's a nice feeling when your center of gravity lifts up.
Even if I can go fast on a bike for 1 min, I can barely sprint that long and surely slowly and I end up exhausted differently. In the end I prefered what running brought me. It may be very subjective though, even if I enjoy all sports, I always had a thing for running.
This is all crude opinion, I'd love if anyone with bio/biomech knowledge could shed light on the subject.
I used to do exactly what you suggest: bike + full workout. I liked it a lot, but it's not integrated as in a sport. It was odd for instance, I had much more "power" than ever, so much that I couldn't run anymore because my thighs were too strong and I had to relearn how to land my foot otherwise I'd miss the ground.
For around 9 weeks I managed to go running for 10km every second day and then my two weeks vacation happened. I'm trying to get back in again because I'm extremely frustrated on days I don't go running. I cannot emphasize enough on the stress relieving part. For me it's around 50 minutes of complete peace of mind where the only things I focus are breathing and moving my body.
One thing I recommend is to track your runs because it's fun and interesting to see your improvement over time. Bonus points if you track your heart rate as well. :)
A smartphone is a bit annoying to carry and use, I might invest in a gps wrist so I can pause / resume with a button.
Right now I'm at 2x2.5km jogging + 5km of walk. And even though I don't have a calorie deficit, I already lost significant amount of fat and got back muscle mass (the bliss of sore muscles right? ;) I'm sure even with a normal diet it's a lot better to have a more active metabolysm as it is now.
I invite you to read literature on the subject:
1. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2556152/?tool=p...
2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2743580/
3. https://www.ncbi.nlm.nih.gov/m/pubmed/16932832/
Note: I am not a doctor, and the literature becomes mixed as you study runners with higher and higher mileage per week. The point is that someone with a healthy weight should not be damaging their joints merely by repeatedly running - proper running involves allowing your feet to fall below you, not ahead of you, where the calves and quads can properly absorb the impact and use the "bounce" from the ground impact to propel forward efficiently. Doing something other than this, like landing on your heel in front of your body, forces your knees to absorb the impact.
If you're running 60, 70 or 80 miles per week there may be degenerative effects on joint health, but if we're speaking realistically that is unlikely to happen for someone just looking to get into shape unless they're a few years in and training for something. I run 30 miles per week and have no plans to significantly increase my mileage - my health and fitness goals are rather more "intense" than most people I know and it takes up a lot of my time (looking at about an hour of running workout per day).
If someone wanted to gain the benefits from jogging, jogging to the store or even commuting by running five days a week would be far, far lower than what appears to be the lower bound on introducing joint degeneration.
I'm going to echo the grandparent comment: if you're not already moving and have a favorite exercise (cycling, swimming), I urge you to consider running. Running every day quite literally changed my life. Dieting is a close second. My mood significantly improved, my sleep improved, every physical activity felt better, etc. After a month of consistent running you even miss it when you don't do it.
Maybe I exagerated, I just know how easy it is to use your muscle and limb chains badly and then stop because it hurts somewhere.
My advice was to start very slow, and avoiding heel is a trigger to think of landing as absorbing, using your calves at first.
Haven't seen anyone mention it, but a more recent, low impact excersize I've picked up recently is golf (walking, no cart, no caddy). I'm currently working of a project that's going on a year behind schedule, and Monday was the third week in a row of a meeting posponed last minute due to collegues having scheduling conflicts that were existing, but not disclosed until late enough to waste an hour of everyones time. Instead of maintaining a few more hours of poor posture at my sitting desk for a noon reschedule, I took off a half day and golfed 18 holes while enjoying the eclipse. My advise: make sure you jog a few miles in the morning, then do your best to tolerate the dangerous sitting posture of your 5 hour work day. OK, now that you've had just about enough sitting for one day, how about a nice afternoon of golf to strech out that lower back?