I am learning to use QGIS and ArcGIS but I can not find the differences between them. What are the differences between the capabilities of QGIS and ArcGIS?
Thats a huge question, so i ll just point out a few things that were important to me. Main differences are that qgis is an opensource application and its free while ArcGIS is a commercial product and it costs a lot of money.
To me important things are the number of supported formats, which is excellent in both and you can even further extend it in qgis with additional libraries, plugins,... also i think that some kind of scripting support is needed in the software because every GIS pro is gonna eventually hit a point where out of the box tools just won't cut it.
The area where i think we have to give ArcGIS an edge is spatial analytics: Arcgis has a ton of tools ready out of the box for you, from the most basic stuff like hillshading, to overlays, map algebra, surface approximation, network analysis,... Of course some of this is available in Qgis, just not to such extent.
For me it was like this: I started out with ArcGIS, then only recently moved to the opensource scene and i got to say, i have in fact no need for ArcGIS anymore, if there is some advanced functionality i need, its probably not available in arcgis anyway so i script it in python-qgis myself. I would say, only go with ArcGIS if you need its analytical functionality, for simple data viewing, symbolisation, simple editing, ur perfectly fine with qgis.
PS: I agree with Simon, its a question of preference
@U2ros makes good points, but I think a few important ones are omitted, for which (as of QGIS 1.8) the typical user's preferences-alone cannot wholly make up the differences between these platforms.
Where ArcGIS has the Edge
Most conspicuously PRINTING. I don't have Arc installed on my primary system these days, but creating print-quality maps in Arc is intuitive and simple compared to counter-intuitive and difficult in QGIS, which I've never been quick to brag of in this respect. (But maybe I'm just doing something wrong? Or haven't had the right "Aha!" moment?)
I also find Arc to be more capable for ADVANCED DIGITIZING, however I should confess I may have made that opinion too many moons ago to be relevant for QGIS 1.8+.
Where QGIS Triumphs
To start.. it's free..
With respect to DATA TRANSLATION AND CONVERSION, particularly for the vector formats, I prefer QGIS. If nothing else, QGIS allows you to input/output WellKnownText (WKT), which can be extremely useful. You can also connect directly to many database engines. (..now more on that..)
MAINTENANCE-PHASE DIGITIZING AND DATA ENTRY, is another area where QGIS provides an advantage. That is, QGIS allows you to connect directly to MySQL or PostGRESql (and others?) without fuss, so you can make simple edits right in your database. You can't do that in Arc.
As honorable mention, QGIS provides a handful of data analysis tools that are not available in the basic ArcView license, but which appear in the higher-cost flavors, ArcEditor and ArcInfo. The tool coming to mind immediately in QGIS is the Vector > Geoprocessing > Difference utility (called Erase in Arc). I suspect there are others.
In Summary I tell people QGIS is great for pros who are converting between data formats, performing various spatial analyses, or desiring to connect directly to tables in MySQL or Post. But if you chiefly want to release print maps and would rather pay for software rather than a human FOSS wizard who can wrangle awesome maps against an open stack, ArcGIS is arguably the better choice.