What is the difference between the order LP filter + Op-Amp and Op-Amp + LP filter in practice?
Indoor lighting usually has a large amount of ripple caused the AC voltage varying lamp brightness at twice the mains frequency. Depending on the particular bulb the variation might be anywhere from 5% to 100%, and could be many times larger than the signal you are trying to detect. A filter attenuates out of band frequencies that could overload the gain stage if it was inserted before the filter. Therefore it is best to filter the signal before (or while) amplifying it, rather than after.    

In your circuit the op amps are configured as inverting amplifiers with an input impedance equal to C1 + R2 for the filter amp and R4 for the voltage amp. The photo-transistor's Collector impedance is very high, so its total output impedance probably won't be much lower than R1 (160k). With the filter amp connected the lower impedance of C1 + R2 will cause a loss of ~20dB in the pass band. 25mV (unloaded) at the photo-transistor should produce an output of ~1V. 

If the voltage amp is inserted first the photo-transistor's impedance (R1) will be in series with R4, reducing the voltage gain to less than 1. The filter amp will now have less loss because it is driven by the low impedance output of the voltage amp, but the final output will still be less than the input. Therefore you will need a much stronger input signal to get a good output level.  

To raise the input impedance of an inverting op-amp circuit you could increase the values of the feedback resistors, isolate it from the source by adding a buffer stage in front of it, or eliminate it by configuring the op amp as a non-inverting amplifier. 

However in your circuit it would be best to keep the filter at the front, and increase the values of its feedback resistors if you want to reduce filter insertion loss. You might also consider AC coupling the filter amp to the voltage amp, which could provide another stage of high pass filtering.