You're talking about asynchronous serial communication (RS232-like). There you have a preset baud rate. Although the PC has a processor running at 2.4GHz, a baud rate of 57600 is still 57600 bits per second. For the PC this is extremely slow, for the UNO it's quite slow, for the Due it's very slow. All of them use exactly the same speed, if they don't no communication will happen. So you don't have to worry about this. It might getting a bit of a problem if you use SoftwareSerial (because there all the work is done using normal instructions, so the processor has to be much faster than the communication speed) but with the hardware USART you're fine with the usual baud rates.