In Eagle, at least in older versions (around 6 I think), the silkscreen layer that is part of the footprint can’t be edited very much. In Kicad you can at least move all the text around, but in Eagle it was only the value and name.
In Kicad you can edit footprints on a per-part basis too, so when the silkscreen is problematic you can just do a custom version that is just for that part on that board. Again, in Eagle I don’t think you could do that… This is going from memory though so don’t quote me.
So for those reasons and more the recommended way to do good silkscreens in Eagle was to use this script that copied the silkscreen layers to new layers that could be freely edited, and then just export those when generating gerbers. Of course the major down-side was that if then moved anything the silkscreen didn’t move along with it.
Anyway, I went back to just using the silk layers in Kicad.