Elaine Pagels, in her Introduction (June 23, 1995) to Thich Nhat Hanh's Living Buddha, Living Christ (1995: Riverhead Books), notes "resonances" between GTh and Buddhist thought. Pagels cites the Prologue and LL. 2, 3, 25, 70, and 108. While predicting that many more resonances are to be found, she observes "comparative study of Buddhism and (early) gnostic Christianity has barely begun" (xxvii).
I present here the resonances noted by Pagels and her very brief comments on paralles to Buddhist thought. In doing so, I would caution that a key distinction between this sort of comparison and traditional textual comparisons is that specific literal parallels are difficult or impossible to identify. This can lead to the conclusion that no dependence can be established.
However the absence of literal parallels, when a thematic parallel seems evident, can also indicate the theme was simply passed orally between cultures of widely differing languages. Or it can indicate intent to disguise or cloak the source (for example, the apparent complete ignorance of the Alexandrian Jesus community in Acts). Or it could mean, as Pagels notes elsewhere, that intense familiarity with canonical texts naturally leads one to think that the nature of other texts is less authentic. Literal textual parallel may not characterize transmission of sayings from Buddhism to Thomas, if that transmission occurred. The close textual parallels among the Synoptics, and their freer parallels in Thomas, may suggest that textual dependence requires some degree of textual literality in parallel. But the Synoptics represent later highly-stylized Roman developments of tradition that cannot reasonably be expected to identify Buddhist sources of the earliest Jesus sayings, if they exist.
Obvously there is a higher risk of proposing dependence based on a thematic parallel when in fact no such dependence exists. Common religious themes may arise independently from similar new social conditions. This is, I think, the gist of the "axial age" - the historical rise of major religious movements in the sixth and fifth centuries BCE - given new life recently by Karen Armstrong.
I think that risk must be accepted for exploration of the origins of Jesus wisdom sayings. Literal textual analysis has shown with outstanding clarity many general processes of emerging diversity during the very active phase of Christian literary development, 70-140 CE. Yet the origins of Thomas and Q sayings, c.50 CE for those who support the "early camp" of original Thomas composition, remain bafflingly obscure. Another way to describe a disciplined but somewhat looser approach, might be "new skins for new wine."
Finally, it can be argued that Pagels' "resonances" are not tangible relationships that can be identified with much precision. I think that is probably true. But it is also very true that both Thomas and Buddhism reject that sort of literal approach to understanding. Jesus in Thomas advises each to "bring forth what is within you" (L.70) and to reject leaders in order to know oneself (L.3). Likewise Buddha advised: "Be an island unto yourself. Take refuge in yourself and not in anything else." (Living Buddha, Living Christ, p. 121).
Okay, on to the sayings and Pagels' brief comments. The translation here is Lambdin-Layton. Important deviations in Pagels' translation are marked "Pagels tr."
P) These are the secret sayings which the living Jesus spoke and which Didymos Judas Thomas wrote down.
PAGELS: "twin" = "fellow child of God" (xxiv).
3) Jesus said, "If those who lead you say, 'See, the Kingdom is in the sky,' then the birds of the sky will precede you. If they say to you, 'It is in the sea,' then the fish will precede you. Rather, the Kingdom is inside of you, and it is outside of you. When you come to know yourselves, then you will become known, and you will realize that it is you who are the sons [Pagels tr. "children"] of the living Father. But if you will not know yourselves, you dwell in poverty and it is you who are that poverty.
PAGELS: "resonates with the Buddhist tradition" (xxiii).
2) Jesus said, "Let him who seeks continue seeking until he finds. When he finds, he will become troubled. When he becomes
troubled, he will be astonished, and he will rule over the All [Pagels tr. "shall come to transcend all things."].
PAGELS: "a path of solitary searching to find understanding" (xxv).
70) If you bring forth what is within you, what you bring forth will save you. If you do not bring forth what is within you, what you do not bring forth will destroy you.
PAGELS: "What is at stake is one's deepest well-being" (xxvi).
25) Love your brother like your soul, guard him like the pupil [Pagels tr. "apple"]of your eye.
PAGELS: "loving compassion for others" (xxvi).
108) He who will drink from my mouth will become like Me. I myself shall become he [Pagels tr. "will become as I am; and I will become that person"], and the things that are hidden will become revealed to him [Pagels tr. "and the mysteries will be revealed to him"].
PAGELS: supports "twin" = "fellow child of God" (xxiv).