Which circuit is better? (Op Amp Question)
Without knowing the opamp types the second circuit will be faster because the RC time constant is massively less in the first stage feedback components. If the second circuit had a 10 nF feedback capacitor then they would be identically fast (again assuming perfect op amps).


  TINA TI simulations say they are identical


Then either you are providing the wrong circuits here or you are doing something wrong in TINA.

Regards noise, the first circuit would be better theoretically because thermal noise from the resistor is not proportional to resistance but the square root. However, you may find that with some opamps, splitting the gain between two stages can overall provide lower noise because of the need to consider the opamp noise gain. Another significant subject.

I would recommend visiting analog devices and using their tool for photodiode amplifiers. Even if your design isn't a photodiode application, the tool will still be very useful.

You can make it single stage or double stage and play tunes with the values to optimise performance. You can select a vast number of opamp so work with this site and hone the design then try to pick opamp they recommend or find alternatives. I don't think you'll be disappointed.