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Hi Song,
The two photodiode circuits you show are not equivalent. The first one, although complex, is a traditional transimpedance amplifier application of a photodiode. It provided an output voltage that is inverted to relative to the input current The second circuit, which doesn't appear to be quite correct, is an attempt at a voltage amplifier. That circuit doesn't appear to be complete and really needs to be configured differently to function.
I am providing a link to a TI/ Burr-Brown Applications Report that discuses photodiode applications. Figure 7 in the report shows two variations on a non-inverting photodiode amplifier. The circuit in 7B being the higher performance of the two:

Follow the advice of the report and you should have good results.
Regards, Thomas
PA - Linear Applications Engineering
Song,
Your first circuit showing the transimpedance amplifier is inverting. The other, which is configured as a voltage amplifier, is non-inverting; but It doesn't appear to be a complete, workable circuit. The Application Bulletin Figure 7 circuits are non-inverting photodiode amplifiers.
Regards, Thomas
PA - Linear Applications Engineering