These are two very interesting poems to compare. In both, the speaker narrates some kind of interaction that he has with two neighbours, but the precise nature of these interactions are very different as we come to discover.
In "Mending Wall," the scenario is that the speaker is walking the edge of his land on one side and his neighbour is walking on his side of the edge of their land. As they go, they repair the wall. However, when they get to a part of the land where it is obvious where the boundary line lies and no harm can be caused by not having a wall, the neighbour only responds by saying "Good fences make good neighbours." This causes the speaker to question this assumption, arguing that whenever we build a wall we wall someone or something in and, conversely, someone or something out, which may cause offence. The description of his neighbour is particularly interesting:
I see him there,
Bringing a stone grasped firmly by the top
In each hand, like an old-stone savage armed.
He moves in darkness it seems to me,
Not of woods only and the shade of trees.
He will not go behind his father's saying,
And he likes having thought of it so well
He says again, "Good fences make good neighbours."
The neighbour is portrayed as being positively prehistoric in clinging on so blindly to his father's saying. He dwells in metaphorical darkness as the speaker compares him to an "old-stone savage armed" and his slavish dependence of accepted tradition, compared to the questioning mind of the speaker.
In "The Axe Helve," on the other hand, the narrator is surprised by an intrusion by his neighbour, who grabs his axe as he is just about to swing it, and then offers to give him a new axe helve because of the poor quality of the first one. Throughout the poem the narrator seems to try and second-guess Baptiste's motives, but eventually concludes that he is just lonely and desiring friendship. The speaker thinks that the axe helve is just an excuse that Baptiste has used "unscrupulously" to bring the speaker into his house. Yet, in spite of his mixed feelings about Baptiste, it is clear that the speaker admires him a lot:
Baptiste knew how to make a short job long
For love of it, and yet not waste time either.
In this somewhat paradoxical statement, we see how the speaker recognises the love and knowledge that Baptiste has of different kinds of woods and axe helves, and his appreciation of the way in which Baptiste savours the moment. The poem narrates how two neighbours connect and share a moment of human warmth and closeness when they had been really strangers before that, which is very different from "Mending Walls," which is all about building barriers between one another. In this poem, barriers are broken down.