Stan09:
I don't see how measuring LED pin frequency relates to original question: how many characters per second can be transferred from Arduino to PC.
31 bytes are transmitted (or placed into a hardware buffer that gets transmitted) per cycle.
Measure the frequency and multiply by 31 to get the average bytes per second.
or, if you like rather:
what maximum port settings on Arduino and receiving terminal allows receiver recognize characters correctly.
That's not how the native USB port works.
Bytes are written into USB packet buffers (on Due, using a hardware register that accesses the buffer in a fifo manner). When the software and drivers on the PC are ready to accept data, the USB host controller on the PC schedules USB bandwidth and sends tokens when the device is allowed to transfer data. If data is waiting in a packet buffer, Due's hardware automatically transfers the data at the full USB speed. The net transfer rate depends on how often the PC software and drivers request data, when the computer's USB host controller chip schedules USB bandwidth (other USB devices are the main factor) and how frequently there is a packet buffer ready to transmit when the host controller sends the token allowing the transfer.
That is absolutely unlike hardware serial used on the programming port, where a fixed baud rate is used and it's up to the receiver to respond to the incoming data quickly enough (or implement additional handshaking lines to cause the transmitter to pause).
It makes no sense, in the context of the native port, to say "allows receiver recognize characters correctly". The speed is fixed at the native USB bit rate, 480 Mbit/sec for Due, but data is only transmitted when all 3 components (receiving software, host controller chip, and Due's packet buffers) are ready to transfer data.
I'd suggest to use Putty as reference receiving terminal program.
Displaying the data in a scrolling window is a poor benchmark for native port. The rate putty requests data will depend on many complex factors of the windowing system and graphic card driver.
the native one accepts any speed settings (as was noticed above, it just ignores it) but real data transfer is very slow, like, few characters per second.
Your measurement of a few characters per second differs tremendously from my measurement of 894 kbytes/sec. I specified exactly how I tested, with complete code for both the Due and PC side. If you would do the same, perhaps someone can try reproducing your test results?