There's a lot of "rules of thumbs out there -- none of which are precise.
They all depend on how you are determining "equal" - and even then it will depend.
Whatever you choose, as long as it's standard for everyone in the challenge, I think that's fair. You just have to assume everyone will take the challenge in the spirit it's intended.
In a VRAA challenge I participate in, they came up with 1 mile = 4 pts for running, and 1 mile = 1.5 pts for bicycling which I found to be very fair for me because if I run or bicycle *at the same intensity*, I can cover a bit over 16 mile in an hour on a bike, or a bit over 6 miles in an hour running.
If you try to compare Calories burned for each - intensity comes into play. There is no precise x = y because they are two very different activities.
Since it's just a fun challenge, again, I think as long as it's standard- don't worry. A 1:3 ratio sounds fair.