mapply
and match
x <- list(a = rnorm(5),
b = rnorm(5))
# $a
# [1] -0.05417899 -0.28140108 -0.51207379 0.73572854 1.24535765
#
# $b
# [1] 1.1580326 0.7900556 0.9595224 -1.2232270 0.6621114
y <- lapply(x, sort)
# $a
# [1] -0.51207379 -0.28140108 -0.05417899 0.73572854 1.24535765
#
# $b
# [1] -1.2232270 0.6621114 0.7900556 0.9595224 1.1580326
mapply(match, y, x)
# a b
# [1,] 3 4
# [2,] 2 5
# [3,] 1 2
# [4,] 4 3
# [5,] 5 1
edit:
z <- as.matrix(mapply(match, y, x))
# a b
# [1,] 3 4
# [2,] 2 5
# [3,] 1 2
# [4,] 4 3
# [5,] 5 1
zz <- LETTERS[1:5]
matrix(zz[z], ncol = 2)
[,1] [,2]
[1,] "C" "D"
[2,] "B" "E"
[3,] "A" "B"
[4,] "D" "C"
[5,] "E" "A"