I am learning to use QGIS and ArcGIS for Desktop. What are the differences between the capabilities of QGIS and ArcGIS in term of processing & representing 3D model?
I've used both and they have similar capabilities, though the tools in ArcGIS are more readily accessible and better presented in my opinion. However, the biggest difference is cost. QGIS is of course free. ArcGIS needs 3D Analyst which represents an additional cost on top of the basic licence. Tools similar to those in 3D analyst can be found in the QGIS processing toolbox courtesy mostly of GRASS and SAGA. In my opinion, the visualisation tools (ArcScene) are easier to use in ArcGIS than QGIS (NViz and others) and slightly more sophisticated, but I consider both limited in this department and when I need to do 3D visualisations I use other 3D software (use the right tool for the job!).
I wouldn't call either QGIS or ArcGIS tools truly 3D though, more 2.5 D, though GRASS (in QGIS) does have some voxel calculations which possibly gives it the edge over ArcGIS (the last time I used it ArcGIS did not offer that). For other QGIS 3D capabilities, have a look at this article.
I think that if these are your choices, it comes down to cost.