As above, the feeling and groove is more important than the finer detail I think, unless it's a tribute band where authenticity is key.
Significant fills recognisable by Joe public should be prominent, but not slavishly so.
I've seen many function bands trying to sound exactly like the original, changing their sounds entirely between songs, and it tends to be rather chintzy.
Ty Segall knows how to do a good cover: rocky, fuzzy, keeping a distinctive riff but making the song his own: