just wondering, in terms of building up stamina and building up leg muscles, which would be more ideal to do???
They're both great for improving stamina and muscle tone, but cycling is going to help more with strength.
I would say running would be better because it takes less time to get "X" amount of exercise done. Plus the lower body muscle group used in running (I would guess) are more similar to the lower body muscle group used in badminton and therefore more direct benefit...
I used to run a lot when I was younger, and it is great for fitness. However, as others mentioned before me it is really hard on the knees. I ended up getting knee surgery to remove the cartilage from my left knee because of wear and tear I am almost certain came from running. I now almost exclusively ride the bike and do stairs for my off-court fitness and have not had any knee issues. It is helpful to do some base level fitness work for badminton to build up your endurance, but I would focus mostly on intervals. Badminton rallies are not that long in reality so long distance running/biking won't offer a similar experience to a badminton rally. I do bike sprints of 30s on 30s off to simulate the effect of a badminton rally. I also do a lot of weights for strength training but that's something for a different post altogether. Emmet BadmintonLife.com
Cycling is a low impact sport, which helps to maintain joint health in contrast to running. Both will improve base aerobic fitness. At a lower level of fitness it can be easier on the person to take up cycling as it can be easier to carry out than running, and the use of gears can make it easier to structure an exercise programme that adapts as the person gets fitter. The other bit that is good for badminton is what is called spinning. Either in special gym classes or on the road by using a lower gear than normal you can get your legs used to fast movements, similar to skipping. This should help improve your footwork around court.