Three Days Grace is a Canadian rock band formed in Norwood, Ontario in 1992. The band's current lineup consists of lead vocalist Adam Gontier, lead guitarist Neil Sanderson, rhythm guitarist Brad Walst, and drummer Barry Stock. Three Days Grace has released six studio albums, with their most recent being Transit of Venus (2012). The band's music is typically described as post-grunge and alternative rock, and they are known for their heavy use of distortion and power chords.
System of a Down is an Armenian-American rock band formed in Glendale, California in 1994. The band's current lineup consists of lead vocalist Serj Tankian, lead guitarist Daron Malakian, rhythm guitarist Shavo Odadjian, and drummer John Dolmayan. System of a Down has released five studio albums, with their most recent being Hypnotize (2005). The band's music is typically described as nu metal and alternative rock, and they are known for their experimental sound and political lyrics.
Ultimately, the question of which band is better is a matter of personal opinion. There are many factors that could affect a person's preference, and there is no right or wrong answer.