This is more of a vague, intuitive type of question, so perhaps there isn't anything too concrete anyone can offer.
I am trying to get a sense of precisely why working with local rings of equal characteristic (char($R$) = char($R/\mathfrak{m}$)) are somehow "easier" than working with rings of mixed characteristic (char($R$) = $0$ but char$(R/\mathfrak{m}) = p$).
I can understand rings of characteristic $0$ being generally nicer than those with positive characteristic, but are there any specific results that are easy to prove in equal characteristic but remain very difficult to see/prove in mixed characteristic? I can think of theorems which are easy to prove in function fields (equal characteristic) but are hard/still not known for $p$-adic fields (mixed characteristic), but I can't think of something unifying the two equal characteristic cases and leaving out the mixed case.