From the Super Mario Wiki
Beanbean coins are the currency of the Beanbean Kingdom found in Mario & Luigi: Superstar Saga and Mario & Luigi: Superstar Saga + Bowser's Minions. They are small, round and made of gold, much like Mushroom coins. The only known differences between them are that these coins are only accepted in the Beanbean Kingdom and are worth a different amount than Mushroom coins.
The exchange rate is incredibly varied and changes frequently. In the beginning of the game Mario & Luigi: Superstar Saga and its remake, the Mario Bros. pay Tolstar around 100 Mushroom coins (depending on how much the player picked up earlier) which translates into 10 Beanbean coins, thus making the exchange rate about 10:1. Later in the game when they win the bet against Prince Peasley, the 99,999,999,999,999 Mushroom coins translate into 99 Beanbean coins, making the exchange rate 1,010,101,010,101:1, a dramatic difference.