Since this hasn't been answered, here goes:
With the exception of SIXAXIS and the PS button not being emulated by the Logitech Button,
I can confirm that the F310 will work properly with the PS3, but mine was only successful
with two things checked before hand.
1) In the case of single player games, it needs to be controller one and without a PS button,
must be manually changed in Accessory Settings. There's no way of knowing the controller's
port number without looking it up in Settings.
2) A small switch on the back of the Logitech controller with X and D options must be on D
before plugging it into the USB port. Otherwise the System will not accept it.
I'd personally recommend this if you have at least one original PS3 controller lying around,
otherwise quitting games and applications will be impossible without shutting down the console.
The joysticks work perfectly fine and The L2/R2 buttons are very similar to the PS3's.
I can't test the F510 but if you follow the same tips mentioned it might work out the same.
Hope this helps anyone else out there with the same question. 
