Network speed between to 2 processors

With correct software the transmit fifo shouldn't be overfilled - since it is an entirely local matter. So are you seeing an error due to it being overfilled, or just getting a transmit requests deferred due to transient lack of space?

Transient lack of space might just be caused by trying to send a lot of packets at once (as might happen with a very large transmit window), especially if the MAC unit isn't being told to actually transmit the packets immediately (it can't be told until the dma? copy of the data into the fifo is complete [1]).

It might be worth doing some tests with a slow network - where is is easy to exceed the network speed - to check the driver (etc) behaves properly.

If you are connecting the systems with a cross over cable, check that the PHYs have actually negotiated the expected speed.

[1] Latency can be improved by giving an early indication - but that can lead to transmit underruns if the dma is stalled for any reason (eg bus contention).