"The Gift of the Magi" is a story about how 2 people love each other so much that they are willing to give up something very precious to them to see the other happy. They think that buying each other something will be the ultimate gift, whereas it was truly the token of their love that was the true gift. In "Luxury", the author goes on about how luxury to some is owning a lot of things, and being in fancy places. To her though, luxury is summed up in the last lines: "you held me/one evening and now I know/the ultimate luxury/of your love".
The connection between the two pieces is the message that love is the ultimate-and most priceless-gift that you can give.