The first design is a single transimpedance-amplifier (TIA) using an ADA4817 and a 1 MOhm resistor. This isn't a great design, since the op-amp is much too fast compared to what is needed/required here. The second design is a 7 kOhm TIA (AD8597) followed by a ~140 V/V gain non-inverting amp (ADA4817). This gives the same total effective gain of ~1 MOhm.
These circuits were designed for a 2 V output with a 2 uA photocurrent produced by about 5 uW of HeNe laser light at 633 nm. The output will hit the "roof" (the positive rail) at about 12 uW of optical power.
The agreement between simulation and experiment is not very good. I suspect my extremely simple LED-test is to blame. I should build a VCSEL circuit which allows testing these and other photodiode receivers to much higher frequencies.