Clipless pedals have several advantages. First, the sole is more rigid so you do not flex into the pedal. Second, it fits your foot differently because your motion and the pressure through the 'drive' phase is quite different. Third, you can 'pull up' and 'push forward', neither of which have direct analogues running. In addition, having yourself 'clipped in' makes the foot more secure and is safer.
There are two things to be careful about. First, you have to remember that your feet are clipped in and you need to twist one to stop (or do a 'track stand' which you are probably not going to learn and which you cannot always apply. Most riders have suffered the ignoble fall at a stop light -- usually your ego is bruised much more than your body. Second, and not so apparent, you can get pedals with various degrees of 'play' or 'float'. I found that I needed one with float rather than one that locks in the position completely. In either case, you also need to align the position of the cleat so that you are pointed in a direction that does not cause the knee to be stressed.
You did ot say what type of bike you are riding. I have both mountain and road bikes and I use my mountain bike shoes around town - they are much easier to walk around on. I use them on my road bike when I am doing around-town stuff even on my road bike, although I use the mountain bike more often in such circumstances.
I raced (mainly Cat III) for several years after injuries made it impossible to run marathons at the pace I desired to race at (sub-6/mile). I found I was actually more successful on the bike, although this was mainly due to living in a area with mountains and mainly doing climbing races).