Label submissions : Demos or previously released material?

So yeah, my band has been playing around and releasing music for more than 2 years now. We've ve seen a very good amount of growth and we're with a local indie label with who we've released a couple of singles and an EP with.

We're planning to do an album next year and we're gonna need as much support as we can get. So we're going to be sending in stuff to slightly bigger labels that focus more on the genre of our music.

So the question is: we have stuff already released, which we are happy with and has contributed a lot to our growth. Is there any point in me recording demos to submit to labels or would our existing material give us more merit?