I think what you should look at it the algorithm used in different software and then compare them with those used in ArcGIS, because there is a lot of interpolation method that can be used in this case, however the Delaunay triangulation is one of the most commonly used. Regarding about the open source software, I think QGIS uses the same algorithm as ArcGIS (I would like to recommend you to check it). R Software can also be used to generate DEM and it includes many packages and libraries (that you can import), however you should read the R documentation to see how those algorithm works. Since R is much flexible and constantly updated and integrated it might have some advanced and well documented algorithm.
In my opinion, at the moment QGIS is one of the best GIS Open Source software, its development is going very fast and with very good quality and its also improving it's documentation. Very flexible!
But my problem is: are those softwares capable of produce a good DEM, made from mass points, contour lines, hard/soft breaklines, soft/hard replace, etc., just like ArcGIS do?
As I can see, QGIS produces a DEM only from contour lines... Is it right?
Now, I understood you. In ArcGIS I know that we can incorporate all (mass points, contour, breaklines/soft and hard etc) into the single model and straightforward.
At least in QGIS 2.18 I think there is no such possibility, however, its possible to interpolate mass point in QGIS. You must download the "interpolation" plugin, which will allows you to customize some parameters.
In addition, I am still believing that R software might have something better then QGIS, however I am not quite familiar with R.
I just have realized that QGIS can make use of all the said data: mass points, contour, breaklines, structure lines and constraints in the plugin that I have just mentioned you (interpolation). Similiar to ArcGIS. Please have a quick look at the link, it provide all the necessary information that you might need.
NOTE: you must add the layer that contain the elevation information (contour), set all parameters and add it to the lower box, and then choose another layer (mass point) set all the parameters and add it to the box, in this successive steps.