In Laurie Lee's poem about apples, he celebrates them - everything about them, even the hollow, worm-eaten ones have a use for a starling, or even for him. It is a joyful, celebratory poem for the most part - full of the richness and heat of summer and the bounty of autumn. It seems as if Robert Frost's poem is more to do with the later end of autumn - as it turns to winter with the first frosts. Perhaps he left the apple harvest a little too late - now he has to rush to gather them in all in one go so the pleasure of it is gone - it is all work. The work has been unrelenting as if some rush meant he could hardly take a break and even has the imprint of the ladder rung under his foot - the stress of it will carry over into his dreams he fears.He has built barriers for his orchard. Lee on the other hand has time aplenty - enough to even watch the apples fall into the grass and watch the creatures that come. He doesn't seem involved in any work to do with them - he is a spectator.
To me, there is not that much that is similar about these poems. Of course, they both have apples in them and talk some about what happens to the apples, but that's about it.
Frost's poem is much less happy than Lee's. To me, the theme of this poem is about how hard it was to pick the apples -- the work of it still sticks in his dreams. So he is looking at the apples as work. He is seeing them (probably they are just metaphors for other things) as things that he has to work hard to get and he is sort of down about it.
In contrast, Lee portrays the apples as natural and symbols of carefree life. The apples just fall and whatever gets them (deer, wasps, worms) gets them -- it's okay. The narrators attitude towards them is that she will take what she gets and it's all okay.
So Frost's poem is about working hard and being a bit sad about how hard and pointless it is. Lee's is about taking things as them come and not stressing.