Updated: Oct 31, 2018
Chords or riffs ? Melodies followed by harmonies and chords, or chords followed by a vocal line (or guitar line etc.) Fit lyrics to a pre-conceived melodic idea or write a song to support a pre-written lyric ? The number of permutations are large.
IMO the archetypal riff aficionados of old were The Rolling Stones and Led Zeppelin, where a guitar riff really defined and drove the song. The brilliant chord-based aficionados were groups like Crowded House or before them The Beatles - or one of my personal favourites, Procol Harum. And others outright experimental, like Elbow for instance. Or if it floats your boat, Scott Walker
There are of course many bands that combine different ways of writing music, and indeed combinations often occurred within bands. I'm sure Jagger and Richards were as good at writing a killer chord change as any other - and often did
The good thing is, when it works, let it work - there is a danger of formularising music, and some on-line courses that tell you how to do it. I suggest trying out the direct alternative to any obvious method or riff or chord change.... and see what happens