Gameplay
When playing with one board, the gameplay is exactly the same, except you switch sides to alternate offense (throwing) and defense (catching). Check out a couple full-game examples with one board:
What are the Pros and Cons of a One Board Set?
More Portable
One board makes carrying the game to the beach, park, or party a little lighter and easier to pack in the car.
Less Expensive
If you're not ready to spend the full retail price for a two-board set, then a one-board is a great entry point to see if you really love the game!
Just as fun (if not more)
For competitive players, switching sides adds an opportunity for a little trash talk and has no impact on gameplay.
More walking
Yes, playing with only one board does add a bit of walking back and forth in order to switch from throwing to catching (and vice versa).
Longer games
Some may prefer the slower pace of a one board game, but others might want to get more throws and catches in!