The obvious thing is that ArcGIS is big money, while QGIS is free. Most (if not all) people using ArcGIS are either students or are working for industry or government agencies.
ArcGIS by the way was once called ARC/INFO -- back in the 1980's when everything related to software was done in CAPITAL letters. The letters "ARC" are not an acronym. They were (and perhaps still are in the ESRI world) what most people would call a path, i.e. a list of coordinates.
I tried it several years ago and was not happy with the experience.
I felt transported to the past (1972 or so) with vibes of FORTRAN
and card decks. Mind you this was just the vibe it gave off.
It gave me a vaguely sticky/crusty feeling.
Sort of like IRAF in the world of astronomical software.
I am sure some fan will read this and hate me.
It is free, and I see it in the Fedora package set, so it would be no big deal to install it. My opinion though is that if you are new to GIS, and looking to get started, you would be much better off to go with QGIS.
Tom's Geology Info / tom@mmto.org