What is the difference between these two CRS and why affects the hillshade rendering?

Question

I am working with a 2m rater files which are in the Swedish SWEREF99 18 00 (EPSG:3011)

The Proj4 information when selecting the CRS with the EPSG code inQGIS is:

+proj=tmerc +lat_0=0 +lon_0=18 +k=1 +x_0=150000 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs

but when I get the files with a .prj file with the text inside

PROJCS["SWEREF99_18_00",GEOGCS["GCS_SWEREF99",DATUM["D_SWEREF99",SPHEROID["GRS_1980",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",18],PARAMETER["scale_factor",1],PARAMETER["false_easting",150000],PARAMETER["false_northing",0],UNIT["Meter",1]]

produces a Proj4 text like this:

+proj=tmerc +lat_0=0 +lon_0=18 +k=1 +x_0=150000 +y_0=0 +ellps=GRS80 +units=m +no_defs

So, the text +towgs84=0,0,0,0,0,0,0 is missing.

My first thought was that the standard EPGS code should be my choice, but the hillshade view does not look nice, below the view when the EPSG 3011 is selected (also as the CRS of the project):

And here when I do not force the selection of the EPSG code (no +towgs84=0,0,0,0,0,0,0 in the CRS description)