The recipient kidney can be implanted into the open area of the abdomen--almost like a "plug and play" (way, way oversimplified) just anchoring it down and attaching the two major vessels and the ureter. The donor must have the surgeon open the abdomen and then dissect intothe retroperitoneal space (not loose within the open abdomen...behind the abdominal cavity and within the tissues.) The donor's body must then adjust to immediate reduction to 1/2 of the prior renal capacity (although usually well tolerated,) while the recipient has an immediate increase in renal function (an improvement.) So assuming no unexpected complications, the surgery itself and immediate post op course is usually easier for the recipient.
Granted, the recipient usually comes into the surgery with poorer health and then the anti-rejection meds must be taken. The longer term recovery is easier for the donor due to these aspects.
Hope this answers the question. Please understand that I am not--at all taking--away from what the recipient must endure, just a tribute to what the donor is willing to sacrifice and what an impressive decision that is.