I noticed the same thing when I switched sports. I think it's because running is a "full body" activity. You're using different legs muscles. The upper body is getting (albeit minor) activity--arms, abs, posterior chain, etc. Let's not forget the constant cardio stress as well.
In cycling, you're sitting. You can coast (i.e. rest). And, you have gears to aid your movement.
Running, unless you stop & walk, is a constant activity. Since you haven't been using those specific muscles associated with running, everything hurts.
When I switched sports, I noticed a big difference in my body. My legs became less bulky. And, my upper body toned as well. (Think about how many cyclists' upper bodies are pudgy & mushy.)
Honestly, I feel so much better running than I ever did cycling. I do miss bicycling a bit, but I only have so much time in the day to exercise.
One of the things I like about running is the simplicity of it. Shoes. I can do it anywhere. Biking, on the other hand, you had to get the bike ready. You had to load it up on the car. You had to drive somewhere, etc. What a headache!