dt1 <- data.table(ids = c(1, 2, 5), col1 = c("A", "B", "F"), col2 = c("B", "F", "G"))
dt2 <- data.table(ids = c(2, 1, 6, 5), col1 = c("B", "A", "K", "L"), col2 = c("F", "G", "M", "G"))

> dt1
   ids col1 col2
1:   1    A    B
2:   2    B    F
3:   5    F    G

> dt2
   ids col1 col2
1:   2    B    F
2:   1    A    G
3:   6    K    M
4:   5    L    G

joint_dt <- merge(dt1, dt2, by = "ids", suffixes = c("", "_old"))
comp_res <- mapply(function(x, y) sum(x == y), joint_dt[, 2:ncol(dt1)], joint_dt[, (ncol(dt1) + 1):ncol(joint_dt)])

> comp_res
col1 col2
   2    2