1. Pretty close in terms of functionality when it comes to rendering, computation. Not close when it comes to out of the box user friendliness (Arc comes packaged with everything and with QGIS you have to tap into a not-as-well-defined plugin ecosystem that is thousands strong to get the functionality). This is either a pro or a con depending on how you look at it. Also ArcGIS out of the box cartography is completely unrivaled compared to QGIS. Similar results can be achieved to ArcGIS when exporting QGIS data to something specializing in vector graphics such as Adobe Illustrator, which is the workflow a lot of people using QGIS do (render vectors/map in QGIS and then take it out to other program).

2. QGIS is actually “better” at interpreting OSM than Arc, simply because people who work on free software like free data and there are many more plugins and tutorials that are based around OSM for QGIS. So it’s not “better” in the sense you might be implying, more like it’s just a much more typical dataset for the QGIS community than Arc and you reap the side benefits of that.

As other poster noted as well, the commercial options for QGIS sat the moment are not very good. I think Desktop GIS is an area that is ripe for Gitlab-esque disruption.