My honest opinion:
Linkin parks version had a huge cultural impact and still stands today as something genuinely popular en masse.
Black Veil Brides in the end has better instrumentation than in the end, with more technical playing of instruments with far better technique, however the general sound, whilst at the time of release was a huge niche, is seemingly fading.
Linkin Park:
Melody:
Guitars: 6/10. It’s catchy but nothing huge going on.
Vocals: 10/10.
Other instruments: 6/10
Rhythm:
Drums: 8/10: whilst not spectacular remains consistent and keeps the song beat catchy
Bass: 8/10, it’s there
Timelessness: 10/10, doesn’t require any real understanding of the music to like and it carries through generations. It was overplayed around me when I was growing up but through time aged well as a certified classic.
Black veil brides:
Melody:
Guitars: 9/10, Really nice lead work, kinda falls a bit flat at times but overall fits the theme of the song to an acceptable level.
Vocals: 7/10 again. Im biased as I don’t like the vocalist personally lol.
Other instruments: 10/10, very symphonic.
Rhythm:
Drums: 8/10: Good rhythm and nice fills.
Bass: 7/10, not very noticeable.
Timelessness: 4/10, has aged and Shows it is from a bygone era of fashion, that whilst still stands today, has evolved beyond what it used to be noticably.
Linkin Park wins for me by a considerable margin.