Had them so bad when running I eventually gave up the sport as nothing seemed to help it, so I concluded that I was simply not put together correctly to tolerate the stresses of running long-term. I don't suffer from splints with cycling, however. The pain of shin splints is your body's way of telling you that it can't tolerate whatever stress is being placed upon it
Not so much the stress of running itself, as having flawed running mechanics. Landing on the heel rather than the fore/midfoot, either because of overstriding or inexperience (we walk with a heel strike, and beginners often see running as fast walking) leads to a higher rate of force development and higher peak forces. Not to mention giving you a nice eccentric contraction of the tibialis anterior with each stride.