HOMER Pro seems to give more optimistic results than HOMER Legacy. Is HOMER Pro less conservative in its simulations? Or was Homer Legacy found to be overly conservative and the Pro version still underestimates the results but to a lesser extent than Legacy?
For identical inputs, HOMER legacy and HOMER Pro will (except for bug fixes) produce exactly the same results. HOMER performs a simple energy balance in each time step. I would encourage you to consult the help documentation included in the HOMER Pro software -- there is a section called "HOMER's Calculations" which explains much of the simulation algorithm. I've attached the articles in a pdf.
I'm not aware of any specific bias in HOMER -- it depends on your model, and you can control how conservative the model is. For example, we simplify battery losses as a simple round-trip efficiency. So, if you select an 81% round trip efficiency, and charge an empty battery with 100 kWh, the battery energy content will be 90 kWh. Then, when you discharge it to empty, you will get 81 kWh back out. Of course, in a real battery, the losses depend on charge and discharge rate, ambient temperature, accumulated battery wear, etc. If you do a technical analysis of your system and conclude that the round-trip efficiency for your battery in your system will never be worse than 81% given all these factors, then you have made a conservative model. You could make the model more aggressive by increasing the round trip efficiency. HOMER itself simply runs the algorithm with your inputs -- whether it is conservative or aggressive depends entirely on your inputs.
This kind of consideration is a great candidate for a sensitivity analysis. You can perform a sensitivity analysis on many of the input variables in HOMER, consider the conservative, nominal, and aggressive cases for an input, and see how the results change with each. If you'd like, consult the help for more details on implementing a sensitivity analysis, or see the attached pdf, "Why Would I Do a Sensitivity Analysis?".
Also, keep in mind, that HOMER is really intended to compare different system architectures and component sizes, and find the best system for a given scenario. The focus is on accurately comparing the relative costs and benefits of different systems, and not on absolute numerical precision. This allows for many simplifying assumptions that makes HOMER fast and powerful.