I ride bicycles and motorbikes.
I suspect that there are less
serious injuries (per hour ridden) on bicycles.
My reasoning:
As said above, your average speed on a bicycle is perhaps 15mph, with a maximum of, say, 35mph (unless you're very fit or live in a
very hilly area

).
A bicycle with decent brakes (hydraulic disc brakes are fairly comon on mountainbikes nowadays) will stop in a shorter distance than a motorbike.
A bicycle is more manoeuvreable at low speeds - it's easier to take evasive action.
On the other hand:
Cyclists generally wear a lot less protective gear. I did a 20 mile bicycle ride this morning wearing shorts, t-shirt and a lightweight helmet. If I'd done the same ride on my motorbike I'd have had a leather jacket, kevlar lined jeans and a full face helmet. Go figure.
The bottom line - I enjoy riding them both. Both activities have an element of risk, but the risk is small enough for me to consider it acceptable. I will continue to ride both as long as I am able to.