It’s been a while (years) since I looked at 3D OC’s code, when I did some work to speed it up for BoneJ that ended up unfortunately forking it (it would be great to merge features back together into some Ops for ImageJ2, but that is another story for another day). The primary difference in the labelling is speed: the result of connected components labelling should be identical. BoneJ achieves labelling with ~O(n) scaling, which means it doesn’t exponentially slow down like the original 3D OC did as you feed it bigger data sets. However, I don’t know how 3D OC performs today.
As for analysis, BoneJ is set up for porous media of which bone is one example - the analysis tools that are there are designed with things like bone’s trabeculae and osteocyte lacunae in mind, which have geometric parallels in other fields. There are quite a number of soil papers and other materials science papers that have used BoneJ for this reason. If you can be more specific about the characteristics you’re interested in, we can guide you towards the most appropriate measurements and discuss implementation differences that might lead to variation in results. Perhaps the most useful thing you could do is run 3D OC and Particle Analyser on the same data and point out any inconsistencies to us here.