Not so much with plot, but more so with the feel of it. More to do with the way the main characters are set up rather than the storyline itself. I don't think it's exclusive to Silence though, but rather the thriller films that we had at that moment in time, which seem to be very few and far between these days. For me, the similarities would be that theme (wonder if it would be classed as a cliche?) of younger, inexperienced female stepping into a highly specialised, potentially dangerous male-dominated profession. Serial killer with unusual, distinctive methods of killing, with a memorable (and creepy) visual appearance. I'd throw the voice into that, too. Childhood trauma, although it's handled differently in both films. Without spoiling it for others, you have the 'confrontation' scene, too. The 'clue-gathering' process and how that mystery unfolds is handled differently in both, too.
In reality, there are probably numerous instances where you could take two films from a similar genre and find similarities, so I'm not saying that they're directly comparable. But, there are certain things that cross-over, in the sense of "if you like film A, you may like film B". I liked Longlegs, because I enjoyed films like Silence of the Lambs, Copycat, Seven, Kiss The Girls, Primal Fear, The Fugitive growing up.