LotR -- Book 1 - Chapter 08 - Fog on the Barrow-Downs

[HerenIstarion]

And as he himself says, his songs are stronger, likely because they stem from Illuvatar as opposed to Melkor

Basically, yes. Minor point - all songs, ultimately, find their source in Illuvatar. It the perversion/lack thereof which makes the right songs stronger (and that in the long run only - cf Felagund/Sauron again)