Bradley - I will chime in while you are waiting for an Laserfiche engineer to respond. RA is the newer of the two technologies. RA is a set of .NET assemblies versus LFSO which is an older set of COM based libraries.
I have used both but for any new project I use RA exclusively. As time permits I will port all of my older LFSO applications to RA as well.
The only drawback that I have encountered is that the documentation in the help files and actual code samples for RA tend to be sparse and in some cases you only have the RA object model as a reference and no examples. Even so, the object model is well laid out and consistent enough that this has not been a problem for me.
Let me know if that helps or if you have additional questions.
New projects should use Repository Access. The API is more uniform and a little more consistent. The only advantage that LFSO would have is if your project is written in a language/platform where COM interop is easier than .Net interop.
The only barrier we have found to using RA is the lack of usage examples. Where can we find something comparable to what LF had in the LFSO documentation?
I don't want to speak for Laserfiche but I would assume that the SDK documentation for the RA model will mature as time goes on. In the interim I am willing to post code examples if you have specific needs.