although word-for-word the three means the same literally,
nuance and actual usage in South Korea differs some-what:
(deep-rooted meanings in each Chinese character do hint)
완쾌 better used when you are well again from light symptoms.
완치 when you have recovered fully from serious ailment, with long-term treatment and/or hospitalization.
쾌차 looks more towards the future for a (re)fresh(ened) start: from now-on, after what you have gone through.
however, in Post-Millennium South Korea amongst chat, tok and blogs:
all three above are mostly used on elders and official correspondence,
as younger generation simply get by all of the above circumstances with
"다 나았니?" albeit: are you fully-recovered now?
( again, in the mass-aging population: "younger" above would mean below 30's)