Project Raster Transformation methods (different calc betweens crs)

Hi there,

I'm quite new working with R. Now Im working with raster data. So far so good. I was transforming data from EPSG-Code 31467 to 4647 using projectRaster(). The result I was comparing with the result from ArcMap. I was wondering: The raster data are not completly congruent.
In ArcMap I can choose between many calculation methods from EPSG-Code 31467 to 4647 (I dont mean 'billinear',...). I mean, how the coordinates are calculated to another system.
So my idea was, that R has a different standard method. But I couldnt find informations about it.
Do you have any idea? Is there a way to change the method?

Cheers,
Denise