Which Christian traditions value the Gospels more than the Epistles? I'm wondering if there are (or were) any Christian communities or traditions that pay (or paid) more attention to the teaching of Jesus than to the teaching of apostles.
The various "New Church" denominations that follow the teachings and Bible interpretations written by Emanuel Swedenborg (1688-1772) give much greater weight to the Gospels (and the book of Revelation) than to the Acts and the Epistles.

As explained in my answer to the question, "What writings are held as 'biblical canon' by Swedenborgians?," in the New Testament, Swedenborg viewed only the four Gospels and the book of Revelation as part of the inspired Word of God. The remaining books in the New Testament he said were "good books of the church," but inspired more in the way that the Holy Spirit inspires a preacher when preaching based on the Word of God.

Because of this belief, Swedenborg based his Christian theology primarily on the Gospels and the book of Revelation (in the New Testament), and only secondarily on the Acts and the Epistles. Swedenborgians have generally followed suit.

Having said that, both Swedenborg himself and various Swedenborgian theologians do also quote from the Acts and the Epistles in supporting and explaining their theology. Swedenborg stated that these books, when rightly understood, also support his theology.